LMFDB - Embedded newform 50.2.d.b.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,2,Mod(11,50)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.399252010106$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			21.2
Root			$1.17421 + 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	50.21
Dual form			50.2.d.b.31.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(1.09089 + 0.792578i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 + 0.587785i) q^{5} +(1.09089 - 0.792578i) q^{6} -0.833366 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.365190 - 1.12394i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(1.09089 + 0.792578i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 + 0.587785i) q^{5} +(1.09089 - 0.792578i) q^{6} -0.833366 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.365190 - 1.12394i) q^{9} +(-0.107666 + 2.23347i) q^{10} +(0.257524 - 0.792578i) q^{11} +(-0.416683 - 1.28242i) q^{12} +(1.41027 + 4.34038i) q^{13} +(-0.257524 + 0.792578i) q^{14} +(-2.81939 - 1.06872i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.41027 + 3.20425i) q^{17} -1.18178 q^{18} +(7.00116 - 5.08664i) q^{19} +(2.09089 + 0.792578i) q^{20} +(-0.909110 - 0.660507i) q^{21} +(-0.674207 - 0.489840i) q^{22} +(1.09089 - 3.35741i) q^{23} -1.34841 q^{24} +(4.30902 - 2.53621i) q^{25} +4.56375 q^{26} +(1.74248 - 5.36279i) q^{27} +(0.674207 + 0.489840i) q^{28} +(-2.64518 - 1.92183i) q^{29} +(-1.88765 + 2.35114i) q^{30} +(-4.85599 + 3.52808i) q^{31} +1.00000 q^{32} +(0.909110 - 0.660507i) q^{33} +(1.68458 + 5.18459i) q^{34} +(1.79793 - 0.489840i) q^{35} +(-0.365190 + 1.12394i) q^{36} +(2.26042 + 6.95685i) q^{37} +(-2.67421 - 8.23036i) q^{38} +(-1.90163 + 5.85263i) q^{39} +(1.39991 - 1.74363i) q^{40} +(0.576909 + 1.77554i) q^{41} +(-0.909110 + 0.660507i) q^{42} -1.63877 q^{43} +(-0.674207 + 0.489840i) q^{44} +(1.44851 + 2.21017i) q^{45} +(-2.85599 - 2.07500i) q^{46} +(0.674207 + 0.489840i) q^{47} +(-0.416683 + 1.28242i) q^{48} -6.30550 q^{49} +(-1.08052 - 4.88185i) q^{50} -7.35074 q^{51} +(1.41027 - 4.34038i) q^{52} +(-5.19972 - 3.77782i) q^{53} +(-4.56186 - 3.31439i) q^{54} +(-0.0897250 + 1.86130i) q^{55} +(0.674207 - 0.489840i) q^{56} +11.6691 q^{57} +(-2.64518 + 1.92183i) q^{58} +(4.18178 + 12.8702i) q^{59} +(1.65275 + 2.52181i) q^{60} +(1.81832 - 5.59621i) q^{61} +(1.85482 + 5.70855i) q^{62} +(0.304337 + 0.936652i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-5.59378 - 8.53513i) q^{65} +(-0.347249 - 1.06872i) q^{66} +(-1.21345 + 0.881621i) q^{67} +5.45140 q^{68} +(3.85105 - 2.79795i) q^{69} +(0.0897250 - 1.86130i) q^{70} +(1.91027 + 1.38790i) q^{71} +(0.956080 + 0.694633i) q^{72} +(-1.02903 + 3.16703i) q^{73} +7.31486 q^{74} +(6.71081 + 0.648503i) q^{75} -8.65392 q^{76} +(-0.214612 + 0.660507i) q^{77} +(4.97854 + 3.61712i) q^{78} +(-4.18178 - 3.03824i) q^{79} +(-1.22570 - 1.87020i) q^{80} +(3.28304 - 2.38527i) q^{81} +1.86692 q^{82} +(9.97971 - 7.25068i) q^{83} +(0.347249 + 1.06872i) q^{84} +(7.63145 - 9.50525i) q^{85} +(-0.506408 + 1.55856i) q^{86} +(-1.36239 - 4.19302i) q^{87} +(0.257524 + 0.792578i) q^{88} +(-2.16491 + 6.66290i) q^{89} +(2.54961 - 0.694633i) q^{90} +(-1.17527 - 3.61712i) q^{91} +(-2.85599 + 2.07500i) q^{92} -8.09363 q^{93} +(0.674207 - 0.489840i) q^{94} +(-12.1147 + 15.0893i) q^{95} +(1.09089 + 0.792578i) q^{96} +(-8.97214 - 6.51864i) q^{97} +(-1.94851 + 5.99689i) q^{98} -0.984855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + q^{11} + 2 q^{12} - 13 q^{13} - q^{14} - 10 q^{15} - 2 q^{16} - 11 q^{17} + 14 q^{18} + 20 q^{19} + 5 q^{20} - 19 q^{21} + q^{22} - 3 q^{23} + 2 q^{24} + 30 q^{25} + 22 q^{26} + 15 q^{27} - q^{28} - 15 q^{29} - 10 q^{30} - 9 q^{31} + 8 q^{32} + 19 q^{33} - q^{34} - 15 q^{35} - q^{36} - 6 q^{37} - 15 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} - 19 q^{42} + 12 q^{43} + q^{44} + 15 q^{45} + 7 q^{46} - q^{47} + 2 q^{48} - 4 q^{49} - 5 q^{50} + 26 q^{51} - 13 q^{52} + 7 q^{53} - 25 q^{54} - 25 q^{55} - q^{56} - 15 q^{58} + 10 q^{59} - 10 q^{60} + 6 q^{61} + 21 q^{62} - 8 q^{63} - 2 q^{64} - 10 q^{65} - 26 q^{66} - 11 q^{67} + 24 q^{68} + 43 q^{69} + 25 q^{70} - 9 q^{71} - 6 q^{72} - 8 q^{73} + 24 q^{74} + 30 q^{75} - 10 q^{76} + 33 q^{77} + 23 q^{78} - 10 q^{79} - 17 q^{81} + 26 q^{82} + 27 q^{83} + 26 q^{84} + 5 q^{85} - 23 q^{86} + q^{88} - 15 q^{89} + 20 q^{90} + q^{91} + 7 q^{92} - 46 q^{93} - q^{94} - 30 q^{95} - 3 q^{96} - 36 q^{97} - 19 q^{98} - 42 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 - 2 * q^8 - q^9 + q^11 + 2 * q^12 - 13 * q^13 - q^14 - 10 * q^15 - 2 * q^16 - 11 * q^17 + 14 * q^18 + 20 * q^19 + 5 * q^20 - 19 * q^21 + q^22 - 3 * q^23 + 2 * q^24 + 30 * q^25 + 22 * q^26 + 15 * q^27 - q^28 - 15 * q^29 - 10 * q^30 - 9 * q^31 + 8 * q^32 + 19 * q^33 - q^34 - 15 * q^35 - q^36 - 6 * q^37 - 15 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 - 19 * q^42 + 12 * q^43 + q^44 + 15 * q^45 + 7 * q^46 - q^47 + 2 * q^48 - 4 * q^49 - 5 * q^50 + 26 * q^51 - 13 * q^52 + 7 * q^53 - 25 * q^54 - 25 * q^55 - q^56 - 15 * q^58 + 10 * q^59 - 10 * q^60 + 6 * q^61 + 21 * q^62 - 8 * q^63 - 2 * q^64 - 10 * q^65 - 26 * q^66 - 11 * q^67 + 24 * q^68 + 43 * q^69 + 25 * q^70 - 9 * q^71 - 6 * q^72 - 8 * q^73 + 24 * q^74 + 30 * q^75 - 10 * q^76 + 33 * q^77 + 23 * q^78 - 10 * q^79 - 17 * q^81 + 26 * q^82 + 27 * q^83 + 26 * q^84 + 5 * q^85 - 23 * q^86 + q^88 - 15 * q^89 + 20 * q^90 + q^91 + 7 * q^92 - 46 * q^93 - q^94 - 30 * q^95 - 3 * q^96 - 36 * q^97 - 19 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	1.09089	+	0.792578i	0.629826	+	0.457595i	0.856340	−	0.516413i	$-0.172733\pi$
$3$	1.09089	+	0.792578i	0.629826	+	0.457595i	−0.226514	+	0.974008i	$0.572733\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.15743	+	0.587785i	−0.964832	+	0.262866i
$5$	−2.15743	+	0.587785i	−0.964832	+	0.262866i
$6$	1.09089	−	0.792578i	0.445354	−	0.323569i
$7$	−0.833366			−0.314983			−0.157491	−	0.987520i	$-0.550341\pi$
$7$	−0.833366			−0.314983			−0.157491	+	0.987520i	$0.550341\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.365190	−	1.12394i	−0.121730	−	0.374646i
$10$	−0.107666	+	2.23347i	−0.0340469	+	0.706287i
$11$	0.257524	−	0.792578i	0.0776465	−	0.238971i	−0.904698	−	0.426054i	$-0.859903\pi$
$11$	0.257524	−	0.792578i	0.0776465	−	0.238971i	0.982344	+	0.187083i	$0.0599033\pi$
$12$	−0.416683	−	1.28242i	−0.120286	−	0.370202i
$13$	1.41027	+	4.34038i	0.391140	+	1.20380i	0.931927	+	0.362645i	$0.118126\pi$
$13$	1.41027	+	4.34038i	0.391140	+	1.20380i	−0.540787	+	0.841159i	$0.681874\pi$
$14$	−0.257524	+	0.792578i	−0.0688262	+	0.211825i
$15$	−2.81939	−	1.06872i	−0.727962	−	0.275943i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.41027	+	3.20425i	−1.06965	+	0.777145i	−0.975849	−	0.218446i	$-0.929901\pi$
$17$	−4.41027	+	3.20425i	−1.06965	+	0.777145i	−0.0937997	+	0.995591i	$0.529901\pi$
$18$	−1.18178			−0.278548
$19$	7.00116	−	5.08664i	1.60618	−	1.16696i	0.732062	−	0.681238i	$-0.238558\pi$
$19$	7.00116	−	5.08664i	1.60618	−	1.16696i	0.874116	−	0.485718i	$-0.161442\pi$
$20$	2.09089	+	0.792578i	0.467537	+	0.177226i
$21$	−0.909110	−	0.660507i	−0.198384	−	0.144134i
$22$	−0.674207	−	0.489840i	−0.143741	−	0.104434i
$23$	1.09089	−	3.35741i	0.227466	−	0.700069i	−0.770566	−	0.637361i	$-0.780026\pi$
$23$	1.09089	−	3.35741i	0.227466	−	0.700069i	0.998032	−	0.0627085i	$-0.0199738\pi$
$24$	−1.34841			−0.275244
$25$	4.30902	−	2.53621i	0.861803	−	0.507242i
$26$	4.56375			0.895024
$27$	1.74248	−	5.36279i	0.335340	−	1.03207i
$28$	0.674207	+	0.489840i	0.127413	+	0.0925711i
$29$	−2.64518	−	1.92183i	−0.491197	−	0.356876i	0.314447	−	0.949275i	$-0.398181\pi$
$29$	−2.64518	−	1.92183i	−0.491197	−	0.356876i	−0.805645	+	0.592399i	$0.798181\pi$
$30$	−1.88765	+	2.35114i	−0.344637	+	0.429258i
$31$	−4.85599	+	3.52808i	−0.872161	+	0.633662i	−0.931166	−	0.364596i	$-0.881207\pi$
$31$	−4.85599	+	3.52808i	−0.872161	+	0.633662i	0.0590050	+	0.998258i	$0.481207\pi$
$32$	1.00000			0.176777
$33$	0.909110	−	0.660507i	0.158256	−	0.114980i
$34$	1.68458	+	5.18459i	0.288902	+	0.889150i
$35$	1.79793	−	0.489840i	0.303905	−	0.0827981i
$36$	−0.365190	+	1.12394i	−0.0608650	+	0.187323i
$37$	2.26042	+	6.95685i	0.371610	+	1.14370i	0.945737	+	0.324932i	$0.105342\pi$
$37$	2.26042	+	6.95685i	0.371610	+	1.14370i	−0.574127	+	0.818766i	$0.694658\pi$
$38$	−2.67421	−	8.23036i	−0.433814	−	1.33514i
$39$	−1.90163	+	5.85263i	−0.304505	+	0.937171i
$40$	1.39991	−	1.74363i	0.221345	−	0.275693i
$41$	0.576909	+	1.77554i	0.0900981	+	0.277293i	0.985945	−	0.167069i	$-0.0534303\pi$
$41$	0.576909	+	1.77554i	0.0900981	+	0.277293i	−0.895847	+	0.444362i	$0.853430\pi$
$42$	−0.909110	+	0.660507i	−0.140279	+	0.101918i
$43$	−1.63877			−0.249910			−0.124955	−	0.992162i	$-0.539879\pi$
$43$	−1.63877			−0.249910			−0.124955	+	0.992162i	$0.539879\pi$
$44$	−0.674207	+	0.489840i	−0.101641	+	0.0738462i
$45$	1.44851	+	2.21017i	0.215931	+	0.329472i
$46$	−2.85599	−	2.07500i	−0.421092	−	0.305941i
$47$	0.674207	+	0.489840i	0.0983432	+	0.0714505i	0.635870	−	0.771796i	$-0.280641\pi$
$47$	0.674207	+	0.489840i	0.0983432	+	0.0714505i	−0.537527	+	0.843247i	$0.680641\pi$
$48$	−0.416683	+	1.28242i	−0.0601430	+	0.185101i
$49$	−6.30550			−0.900786
$50$	−1.08052	−	4.88185i	−0.152809	−	0.690398i
$51$	−7.35074			−1.02931
$52$	1.41027	−	4.34038i	0.195570	−	0.601902i
$53$	−5.19972	−	3.77782i	−0.714237	−	0.518923i	0.170301	−	0.985392i	$-0.445526\pi$
$53$	−5.19972	−	3.77782i	−0.714237	−	0.518923i	−0.884538	+	0.466469i	$0.845526\pi$
$54$	−4.56186	−	3.31439i	−0.620791	−	0.451031i
$55$	−0.0897250	+	1.86130i	−0.0120985	+	0.250978i
$56$	0.674207	−	0.489840i	0.0900947	−	0.0654576i
$57$	11.6691			1.54560
$58$	−2.64518	+	1.92183i	−0.347329	+	0.252349i
$59$	4.18178	+	12.8702i	0.544421	+	1.67556i	0.722362	+	0.691515i	$0.243057\pi$
$59$	4.18178	+	12.8702i	0.544421	+	1.67556i	−0.177940	+	0.984041i	$0.556943\pi$
$60$	1.65275	+	2.52181i	0.213369	+	0.325564i
$61$	1.81832	−	5.59621i	0.232812	−	0.716521i	−0.764592	−	0.644514i	$-0.777060\pi$
$61$	1.81832	−	5.59621i	0.232812	−	0.716521i	0.997404	−	0.0720066i	$-0.0229403\pi$
$62$	1.85482	+	5.70855i	0.235563	+	0.724987i
$63$	0.304337	+	0.936652i	0.0383428	+	0.118007i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−5.59378	−	8.53513i	−0.693823	−	1.05865i
$66$	−0.347249	−	1.06872i	−0.0427434	−	0.131551i
$67$	−1.21345	+	0.881621i	−0.148246	+	0.107707i	−0.659436	−	0.751761i	$-0.729205\pi$
$67$	−1.21345	+	0.881621i	−0.148246	+	0.107707i	0.511190	+	0.859468i	$0.329205\pi$
$68$	5.45140			0.661079
$69$	3.85105	−	2.79795i	0.463612	−	0.336834i
$70$	0.0897250	−	1.86130i	0.0107242	−	0.222468i
$71$	1.91027	+	1.38790i	0.226708	+	0.164713i	0.695341	−	0.718680i	$-0.255253\pi$
$71$	1.91027	+	1.38790i	0.226708	+	0.164713i	−0.468633	+	0.883393i	$0.655253\pi$
$72$	0.956080	+	0.694633i	0.112675	+	0.0818632i
$73$	−1.02903	+	3.16703i	−0.120439	+	0.370672i	−0.993043	−	0.117756i	$-0.962430\pi$
$73$	−1.02903	+	3.16703i	−0.120439	+	0.370672i	0.872604	+	0.488429i	$0.162430\pi$
$74$	7.31486			0.850335
$75$	6.71081	+	0.648503i	0.774897	+	0.0748827i
$76$	−8.65392			−0.992672
$77$	−0.214612	+	0.660507i	−0.0244573	+	0.0752718i
$78$	4.97854	+	3.61712i	0.563709	+	0.409559i
$79$	−4.18178	−	3.03824i	−0.470487	−	0.341829i	0.327144	−	0.944974i	$-0.393914\pi$
$79$	−4.18178	−	3.03824i	−0.470487	−	0.341829i	−0.797631	+	0.603146i	$0.793914\pi$
$80$	−1.22570	−	1.87020i	−0.137037	−	0.209095i
$81$	3.28304	−	2.38527i	0.364782	−	0.265030i
$82$	1.86692			0.206167
$83$	9.97971	−	7.25068i	1.09542	−	0.795866i	0.115110	−	0.993353i	$-0.463278\pi$
$83$	9.97971	−	7.25068i	1.09542	−	0.795866i	0.980306	+	0.197487i	$0.0632780\pi$
$84$	0.347249	+	1.06872i	0.0378880	+	0.116607i
$85$	7.63145	−	9.50525i	0.827747	−	1.03099i
$86$	−0.506408	+	1.55856i	−0.0546074	+	0.168064i
$87$	−1.36239	−	4.19302i	−0.146064	−	0.449539i
$88$	0.257524	+	0.792578i	0.0274522	+	0.0844891i
$89$	−2.16491	+	6.66290i	−0.229480	+	0.706266i	0.768326	+	0.640058i	$0.221090\pi$
$89$	−2.16491	+	6.66290i	−0.229480	+	0.706266i	−0.997806	+	0.0662073i	$0.978910\pi$
$90$	2.54961	−	0.694633i	0.268752	−	0.0732207i
$91$	−1.17527	−	3.61712i	−0.123202	−	0.379178i
$92$	−2.85599	+	2.07500i	−0.297757	+	0.216333i
$93$	−8.09363			−0.839270
$94$	0.674207	−	0.489840i	0.0695391	−	0.0505231i
$95$	−12.1147	+	15.0893i	−1.24294	+	1.54813i
$96$	1.09089	+	0.792578i	0.111338	+	0.0808921i
$97$	−8.97214	−	6.51864i	−0.910982	−	0.661867i	0.0302807	−	0.999541i	$-0.490360\pi$
$97$	−8.97214	−	6.51864i	−0.910982	−	0.661867i	−0.941263	+	0.337674i	$0.890360\pi$
$98$	−1.94851	+	5.99689i	−0.196829	+	0.605777i
$99$	−0.984855			−0.0989816
$100$	−4.97682	−	0.480938i	−0.497682	−	0.0480938i
$101$	12.7085			1.26454			0.632272	−	0.774746i	$-0.282122\pi$
$101$	12.7085			1.26454			0.632272	+	0.774746i	$0.282122\pi$
$102$	−2.27150	+	6.99097i	−0.224912	+	0.692209i
$103$	−5.67537	−	4.12340i	−0.559211	−	0.406291i	0.271959	−	0.962309i	$-0.412328\pi$
$103$	−5.67537	−	4.12340i	−0.559211	−	0.406291i	−0.831170	+	0.556018i	$0.812328\pi$
$104$	−3.69215	−	2.68250i	−0.362045	−	0.263041i
$105$	2.34958	+	0.890637i	0.229295	+	0.0869173i
$106$	−5.19972	+	3.77782i	−0.505042	+	0.366934i
$107$	−10.7700			−1.04118			−0.520589	−	0.853807i	$-0.674288\pi$
$107$	−10.7700			−1.04118			−0.520589	+	0.853807i	$0.674288\pi$
$108$	−4.56186	+	3.31439i	−0.438965	+	0.318927i
$109$	−3.28655	−	10.1150i	−0.314795	−	0.968838i	−0.975839	−	0.218491i	$-0.929886\pi$
$109$	−3.28655	−	10.1150i	−0.314795	−	0.968838i	0.661044	−	0.750347i	$-0.270114\pi$
$110$	1.74248	+	0.660507i	0.166139	+	0.0629769i
$111$	−3.04798	+	9.38071i	−0.289301	+	0.890378i
$112$	−0.257524	−	0.792578i	−0.0243337	−	0.0748916i
$113$	0.538232	+	1.65651i	0.0506326	+	0.155831i	0.973176	−	0.230063i	$-0.0738931\pi$
$113$	0.538232	+	1.65651i	0.0506326	+	0.155831i	−0.922543	+	0.385894i	$0.873893\pi$
$114$	3.60594	−	11.0979i	0.337727	−	1.03942i
$115$	−0.380081	+	7.88460i	−0.0354428	+	0.735242i
$116$	1.01037	+	3.10959i	0.0938103	+	0.288718i
$117$	4.36331	−	3.17013i	0.403388	−	0.293078i
$118$	13.5325			1.24577
$119$	3.67537	−	2.67031i	0.336921	−	0.244787i
$120$	2.90911	−	0.792578i	0.265564	−	0.0723521i
$121$	8.33733	+	6.05742i	0.757939	+	0.550675i
$122$	−4.76042	−	3.45865i	−0.430988	−	0.313131i
$123$	−0.777913	+	2.39417i	−0.0701420	+	0.215875i
$124$	6.00233			0.539025
$125$	−7.80566	+	8.00448i	−0.698159	+	0.715942i
$126$	0.984855			0.0877378
$127$	1.75112	−	5.38938i	0.155386	−	0.478230i	−0.842813	−	0.538206i	$-0.819102\pi$
$127$	1.75112	−	5.38938i	0.155386	−	0.478230i	0.998200	+	0.0599756i	$0.0191023\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−1.78772	−	1.29885i	−0.157400	−	0.114358i
$130$	−9.84597	+	2.68250i	−0.863548	+	0.235271i
$131$	13.3281	−	9.68345i	1.16448	−	0.846047i	0.174145	−	0.984720i	$-0.444284\pi$
$131$	13.3281	−	9.68345i	1.16448	−	0.846047i	0.990338	+	0.138673i	$0.0442838\pi$
$132$	−1.12372			−0.0978074
$133$	−5.83453	+	4.23903i	−0.505918	+	0.367571i
$134$	0.463496	+	1.42649i	0.0400399	+	0.123230i
$135$	−0.607103	+	12.5940i	−0.0522511	+	1.08392i
$136$	1.68458	−	5.18459i	0.144451	−	0.444575i
$137$	−0.894062	−	2.75164i	−0.0763849	−	0.235088i	0.905572	−	0.424192i	$-0.139442\pi$
$137$	−0.894062	−	2.75164i	−0.0763849	−	0.235088i	−0.981957	+	0.189104i	$0.939442\pi$
$138$	−1.47097	−	4.52718i	−0.125217	−	0.385379i
$139$	1.54184	−	4.74531i	0.130778	−	0.402492i	−0.864132	−	0.503266i	$-0.832132\pi$
$139$	1.54184	−	4.74531i	0.130778	−	0.402492i	0.994909	+	0.100774i	$0.0321318\pi$
$140$	−1.74248	−	0.660507i	−0.147266	−	0.0558230i
$141$	0.347249	+	1.06872i	0.0292437	+	0.0900027i
$142$	1.91027	−	1.38790i	0.160307	−	0.116470i
$143$	3.80327			0.318045
$144$	0.956080	−	0.694633i	0.0796733	−	0.0578861i
$145$	6.83642	+	2.59143i	0.567733	+	0.215206i
$146$	2.69403	+	1.95733i	0.222960	+	0.161990i
$147$	−6.87861	−	4.99760i	−0.567338	−	0.412195i
$148$	2.26042	−	6.95685i	0.185805	−	0.571849i
$149$	2.00579			0.164320			0.0821602	−	0.996619i	$-0.473818\pi$
$149$	2.00579			0.164320			0.0821602	+	0.996619i	$0.473818\pi$
$150$	2.69052	−	6.18196i	0.219680	−	0.504755i
$151$	−1.96971			−0.160293			−0.0801463	−	0.996783i	$-0.525539\pi$
$151$	−1.96971			−0.160293			−0.0801463	+	0.996783i	$0.525539\pi$
$152$	−2.67421	+	8.23036i	−0.216907	+	0.667571i
$153$	5.21197	+	3.78672i	0.421363	+	0.306138i
$154$	0.561861	+	0.408216i	0.0452760	+	0.0328950i
$155$	8.40270	−	10.4659i	0.674921	−	0.840639i
$156$	4.97854	−	3.61712i	0.398603	−	0.289602i
$157$	7.78467			0.621284			0.310642	−	0.950527i	$-0.399456\pi$
$157$	7.78467			0.621284			0.310642	+	0.950527i	$0.399456\pi$
$158$	−4.18178	+	3.03824i	−0.332685	+	0.241709i
$159$	−2.67811	−	8.24237i	−0.212388	−	0.653662i
$160$	−2.15743	+	0.587785i	−0.170560	+	0.0464685i
$161$	−0.909110	+	2.79795i	−0.0716479	+	0.220510i
$162$	−1.25401	−	3.85944i	−0.0985242	−	0.303226i
$163$	4.35589	+	13.4060i	0.341180	+	1.05004i	0.963597	+	0.267358i	$0.0861505\pi$
$163$	4.35589	+	13.4060i	0.341180	+	1.05004i	−0.622418	+	0.782685i	$0.713849\pi$
$164$	0.576909	−	1.77554i	0.0450490	−	0.138647i
$165$	−1.57311	+	1.95936i	−0.122466	+	0.152536i
$166$	−3.81191	−	11.7319i	−0.295862	−	0.910568i
$167$	6.59846	−	4.79406i	0.510604	−	0.370976i	−0.302448	−	0.953166i	$-0.597804\pi$
$167$	6.59846	−	4.79406i	0.510604	−	0.370976i	0.813053	+	0.582190i	$0.197804\pi$
$168$	1.12372			0.0866970
$169$	−6.33280	+	4.60105i	−0.487139	+	0.353927i
$170$	−6.68178	−	10.1952i	−0.512469	−	0.781938i
$171$	−8.27383	−	6.01129i	−0.632716	−	0.459695i
$172$	1.32579	+	0.963245i	0.101091	+	0.0734467i
$173$	−0.773580	+	2.38084i	−0.0588142	+	0.181012i	−0.976147	−	0.217109i	$-0.930337\pi$
$173$	−0.773580	+	2.38084i	−0.0588142	+	0.181012i	0.917333	+	0.398120i	$0.130337\pi$
$174$	−4.40880			−0.334230
$175$	−3.59099	+	2.11359i	−0.271453	+	0.159773i
$176$	0.833366			0.0628173
$177$	−5.63877	+	17.3544i	−0.423836	+	1.30443i
$178$	5.66780	+	4.11790i	0.424820	+	0.308649i
$179$	16.2067	+	11.7749i	1.21135	+	0.880096i	0.995352	−	0.0962986i	$-0.0307004\pi$
$179$	16.2067	+	11.7749i	1.21135	+	0.880096i	0.215995	+	0.976394i	$0.430700\pi$
$180$	0.127237	−	2.63947i	0.00948371	−	0.196735i
$181$	−6.37367	+	4.63074i	−0.473751	+	0.344201i	−0.798902	−	0.601462i	$-0.794585\pi$
$181$	−6.37367	+	4.63074i	−0.473751	+	0.344201i	0.325150	+	0.945662i	$0.394585\pi$
$182$	−3.80327			−0.281917
$183$	6.41901	−	4.66369i	0.474507	−	0.344750i
$184$	1.09089	+	3.35741i	0.0804215	+	0.247512i
$185$	−8.96583	−	13.6803i	−0.659181	−	1.00579i
$186$	−2.50107	+	7.69750i	−0.183387	+	0.564408i
$187$	1.40387	+	4.32066i	0.102661	+	0.315958i
$188$	−0.257524	−	0.792578i	−0.0187819	−	0.0578047i
$189$	−1.45212	+	4.46916i	−0.105626	+	0.325084i
$190$	10.6071	+	16.1846i	0.769520	+	1.17415i
$191$	−1.63013	−	5.01702i	−0.117952	−	0.363019i	0.874599	−	0.484847i	$-0.161125\pi$
$191$	−1.63013	−	5.01702i	−0.117952	−	0.363019i	−0.992551	+	0.121827i	$0.961125\pi$
$192$	1.09089	−	0.792578i	0.0787282	−	0.0571994i
$193$	−13.4461			−0.967873			−0.483937	−	0.875103i	$-0.660793\pi$
$193$	−13.4461			−0.967873			−0.483937	+	0.875103i	$0.660793\pi$
$194$	−8.97214	+	6.51864i	−0.644162	+	0.468011i
$195$	0.662556	−	13.7444i	0.0474466	−	0.984257i
$196$	5.10126	+	3.70628i	0.364376	+	0.264734i
$197$	4.39991	+	3.19672i	0.313480	+	0.227757i	0.733388	−	0.679810i	$-0.237938\pi$
$197$	4.39991	+	3.19672i	0.313480	+	0.227757i	−0.419908	+	0.907567i	$0.637938\pi$
$198$	−0.304337	+	0.936652i	−0.0216283	+	0.0665650i
$199$	−17.4090			−1.23409			−0.617045	−	0.786927i	$-0.711671\pi$
$199$	−17.4090			−1.23409			−0.617045	+	0.786927i	$0.711671\pi$
$200$	−1.99532	+	4.58462i	−0.141090	+	0.324181i
$201$	−2.02249			−0.142655
$202$	3.92715	−	12.0865i	0.276313	−	0.850404i
$203$	2.20440	+	1.60159i	0.154719	+	0.112410i
$204$	5.94688	+	4.32066i	0.416365	+	0.302507i
$205$	−2.28828	−	3.49152i	−0.159820	−	0.243858i
$206$	−5.67537	+	4.12340i	−0.395422	+	0.287291i
$207$	−4.17191			−0.289968
$208$	−3.69215	+	2.68250i	−0.256004	+	0.185998i
$209$	−2.22859	−	6.85890i	−0.154155	−	0.474440i
$210$	1.57311	−	1.95936i	0.108555	−	0.135209i
$211$	−0.0834142	+	0.256723i	−0.00574247	+	0.0176735i	−0.953887	−	0.300167i	$-0.902958\pi$
$211$	−0.0834142	+	0.256723i	−0.00574247	+	0.0176735i	0.948144	+	0.317840i	$0.102958\pi$
$212$	1.98612	+	6.11264i	0.136407	+	0.419818i
$213$	0.983884	+	3.02808i	0.0674146	+	0.207481i
$214$	−3.32812	+	10.2429i	−0.227506	+	0.700191i
$215$	3.53553	−	0.963245i	0.241121	−	0.0656928i
$216$	1.74248	+	5.36279i	0.118560	+	0.364892i
$217$	4.04681	−	2.94018i	0.274716	−	0.199593i
$218$	−10.6355			−0.720328
$219$	−3.63267	+	2.63929i	−0.245473	+	0.178347i
$220$	1.16663	−	1.45309i	0.0786545	−	0.0979670i
$221$	−20.1274	−	14.6234i	−1.35391	−	0.983676i
$222$	7.97971	+	5.79760i	0.535563	+	0.389109i
$223$	7.16032	−	22.0372i	0.479491	−	1.47572i	−0.360313	−	0.932831i	$-0.617330\pi$
$223$	7.16032	−	22.0372i	0.479491	−	1.47572i	0.839804	−	0.542889i	$-0.182670\pi$
$224$	−0.833366			−0.0556816
$225$	−4.42416	−	3.91687i	−0.294944	−	0.261125i
$226$	1.74176			0.115860
$227$	−0.0780741	+	0.240287i	−0.00518196	+	0.0159484i	−0.953614	−	0.301032i	$-0.902669\pi$
$227$	−0.0780741	+	0.240287i	−0.00518196	+	0.0159484i	0.948432	+	0.316980i	$0.102669\pi$
$228$	−9.44047	−	6.85890i	−0.625210	−	0.454242i
$229$	17.0625	+	12.3966i	1.12752	+	0.819191i	0.985332	−	0.170649i	$-0.0545864\pi$
$229$	17.0625	+	12.3966i	1.12752	+	0.819191i	0.142187	+	0.989840i	$0.454586\pi$
$230$	7.38125	+	2.79795i	0.486705	+	0.184492i
$231$	−0.757621	+	0.550444i	−0.0498478	+	0.0362166i
$232$	3.26962			0.214661
$233$	11.8178	−	8.58610i	0.774207	−	0.562494i	−0.129028	−	0.991641i	$-0.541186\pi$
$233$	11.8178	−	8.58610i	0.774207	−	0.562494i	0.903235	+	0.429147i	$0.141186\pi$
$234$	−1.66663	−	5.12937i	−0.108951	−	0.335318i
$235$	−1.74248	−	0.660507i	−0.113667	−	0.0430867i
$236$	4.18178	−	12.8702i	0.272211	−	0.837778i
$237$	−2.15382	−	6.62877i	−0.139906	−	0.430585i
$238$	−1.40387	−	4.32066i	−0.0909992	−	0.280067i
$239$	1.79793	−	5.53346i	0.116298	−	0.357930i	−0.875917	−	0.482461i	$-0.839743\pi$
$239$	1.79793	−	5.53346i	0.116298	−	0.357930i	0.992216	+	0.124532i	$0.0397429\pi$
$240$	0.145178	−	3.01165i	0.00937121	−	0.194401i
$241$	4.24254	+	13.0572i	0.273286	+	0.841087i	0.989668	+	0.143379i	$0.0457968\pi$
$241$	4.24254	+	13.0572i	0.273286	+	0.841087i	−0.716382	+	0.697708i	$0.754203\pi$
$242$	8.33733	−	6.05742i	0.535944	−	0.389386i
$243$	−11.4444			−0.734157
$244$	−4.76042	+	3.45865i	−0.304754	+	0.221417i
$245$	13.6037	−	3.70628i	0.869108	−	0.236786i
$246$	2.03660	+	1.47968i	0.129849	+	0.0943408i
$247$	31.9515	+	23.2141i	2.03303	+	1.47708i
$248$	1.85482	−	5.70855i	0.117781	−	0.362494i
$249$	16.6335			1.05410
$250$	5.20063	+	9.89714i	0.328917	+	0.625950i
$251$	−15.8938			−1.00320			−0.501602	−	0.865098i	$-0.667256\pi$
$251$	−15.8938			−1.00320			−0.501602	+	0.865098i	$0.667256\pi$
$252$	0.304337	−	0.936652i	0.0191714	−	0.0590036i
$253$	−2.38008	−	1.72923i	−0.149634	−	0.108716i
$254$	−4.58448	−	3.33082i	−0.287656	−	0.208994i
$255$	15.8587	−	4.32066i	0.993112	−	0.270570i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.31253			−0.144252			−0.0721259	−	0.997396i	$-0.522978\pi$
$257$	−2.31253			−0.144252			−0.0721259	+	0.997396i	$0.522978\pi$
$258$	−1.78772	+	1.29885i	−0.111298	+	0.0808631i
$259$	−1.88375	−	5.79760i	−0.117051	−	0.360245i
$260$	−0.491360	+	10.1930i	−0.0304728	+	0.632144i
$261$	−1.19403	+	3.67485i	−0.0739088	+	0.227468i
$262$	−5.09089	−	15.6681i	−0.314516	−	0.967981i
$263$	−6.63129	−	20.4090i	−0.408903	−	1.25847i	−0.917592	−	0.397524i	$-0.869870\pi$
$263$	−6.63129	−	20.4090i	−0.408903	−	1.25847i	0.508689	−	0.860951i	$-0.330130\pi$
$264$	−0.347249	+	1.06872i	−0.0213717	+	0.0657754i
$265$	13.4386	+	5.09406i	0.825526	+	0.312926i
$266$	2.22859	+	6.85890i	0.136644	+	0.420546i
$267$	−7.64254	+	5.55263i	−0.467716	+	0.339815i
$268$	1.49990			0.0916212
$269$	−17.3020	+	12.5706i	−1.05492	+	0.766445i	−0.973142	−	0.230206i	$-0.926060\pi$
$269$	−17.3020	+	12.5706i	−1.05492	+	0.766445i	−0.0817787	+	0.996651i	$0.526060\pi$
$270$	11.7900	+	4.46916i	0.717519	+	0.271985i
$271$	21.1400	+	15.3591i	1.28417	+	0.933001i	0.999670	−	0.0256766i	$-0.00817402\pi$
$271$	21.1400	+	15.3591i	1.28417	+	0.933001i	0.284495	+	0.958677i	$0.408174\pi$
$272$	−4.41027	−	3.20425i	−0.267412	−	0.194286i
$273$	1.58476	−	4.87738i	0.0959139	−	0.295192i
$274$	−2.89324			−0.174787
$275$	−0.900470	−	4.06837i	−0.0543004	−	0.245332i
$276$	−4.76016			−0.286528
$277$	−5.76220	+	17.7342i	−0.346217	+	1.06555i	0.614712	+	0.788752i	$0.289272\pi$
$277$	−5.76220	+	17.7342i	−0.346217	+	1.06555i	−0.960929	+	0.276795i	$0.910728\pi$
$278$	−4.03660	−	2.93276i	−0.242099	−	0.175895i
$279$	5.73871	+	4.16941i	0.343567	+	0.249616i
$280$	−1.16663	+	1.45309i	−0.0697197	+	0.0868384i
$281$	−11.9886	+	8.71023i	−0.715180	+	0.519609i	−0.884841	−	0.465894i	$-0.845733\pi$
$281$	−11.9886	+	8.71023i	−0.715180	+	0.519609i	0.169661	+	0.985503i	$0.445733\pi$
$282$	1.12372			0.0669167
$283$	−12.7663	+	9.27523i	−0.758875	+	0.551355i	−0.898565	−	0.438840i	$-0.855389\pi$
$283$	−12.7663	+	9.27523i	−0.758875	+	0.551355i	0.139690	+	0.990195i	$0.455389\pi$
$284$	−0.729660	−	2.24566i	−0.0432974	−	0.133256i
$285$	−25.1752	+	6.85890i	−1.49125	+	0.406286i
$286$	1.17527	−	3.61712i	0.0694955	−	0.213885i
$287$	−0.480776	−	1.47968i	−0.0283793	−	0.0873426i
$288$	−0.365190	−	1.12394i	−0.0215190	−	0.0662288i
$289$	3.93000	−	12.0953i	0.231177	−	0.711489i
$290$	4.57716	−	5.70102i	0.268780	−	0.334776i
$291$	−4.62108	−	14.2222i	−0.270893	−	0.833722i
$292$	2.69403	−	1.95733i	0.157656	−	0.114544i
$293$	18.4003			1.07496			0.537479	−	0.843277i	$-0.319377\pi$
$293$	18.4003			1.07496			0.537479	+	0.843277i	$0.319377\pi$
$294$	−6.87861	+	4.99760i	−0.401169	+	0.291466i
$295$	−16.5868	−	25.3086i	−0.965722	−	1.47352i
$296$	−5.91785	−	4.29957i	−0.343968	−	0.249907i
$297$	−3.80170	−	2.76210i	−0.220597	−	0.160273i
$298$	0.619822	−	1.90761i	0.0359053	−	0.110505i
$299$	16.1109			0.931718
$300$	−5.04798	−	4.46916i	−0.291445	−	0.258027i
$301$	1.36569			0.0787173
$302$	−0.608674	+	1.87330i	−0.0350252	+	0.107797i
$303$	13.8636	+	10.0725i	0.796443	+	0.578649i
$304$	7.00116	+	5.08664i	0.401544	+	0.291739i
$305$	−0.633527	+	13.1422i	−0.0362757	+	0.752521i
$306$	5.21197	−	3.78672i	0.297949	−	0.216472i
$307$	−34.1179			−1.94721			−0.973606	−	0.228237i	$-0.926704\pi$
$307$	−34.1179			−1.94721			−0.973606	+	0.228237i	$0.926704\pi$
$308$	0.561861	−	0.408216i	0.0320150	−	0.0232603i
$309$	−2.92309	−	8.99635i	−0.166289	−	0.511784i
$310$	−7.35705	−	11.2256i	−0.417853	−	0.637570i
$311$	−4.02893	+	12.3998i	−0.228460	+	0.703127i	0.769462	+	0.638692i	$0.220524\pi$
$311$	−4.02893	+	12.3998i	−0.228460	+	0.703127i	−0.997922	+	0.0644345i	$0.979476\pi$
$312$	−1.90163	−	5.85263i	−0.107659	−	0.331340i
$313$	1.07619	+	3.31217i	0.0608298	+	0.187215i	0.976854	−	0.213909i	$-0.0686196\pi$
$313$	1.07619	+	3.31217i	0.0608298	+	0.187215i	−0.916024	+	0.401124i	$0.868620\pi$
$314$	2.40559	−	7.40366i	0.135756	−	0.417813i
$315$	−1.20714	−	1.84188i	−0.0680144	−	0.103778i
$316$	1.59730	+	4.91598i	0.0898550	+	0.276545i
$317$	−3.89975	+	2.83333i	−0.219032	+	0.159136i	−0.691891	−	0.722002i	$-0.743222\pi$
$317$	−3.89975	+	2.83333i	−0.219032	+	0.159136i	0.472859	+	0.881138i	$0.343222\pi$
$318$	−8.66654			−0.485995
$319$	−2.20440	+	1.60159i	−0.123423	+	0.0896719i
$320$	−0.107666	+	2.23347i	−0.00601870	+	0.124855i
$321$	−11.7489	−	8.53609i	−0.655761	−	0.476438i
$322$	2.38008	+	1.72923i	0.132637	+	0.0963662i
$323$	−14.5782	+	44.8670i	−0.811151	+	2.49647i
$324$	−4.05806			−0.225448
$325$	17.0850	+	15.1260i	0.947707	+	0.839040i
$326$	14.0960			0.780703
$327$	4.43163	−	13.6392i	0.245070	−	0.754248i
$328$	−1.51037	−	1.09735i	−0.0833961	−	0.0605908i
$329$	−0.561861	−	0.408216i	−0.0309764	−	0.0225057i
$330$	1.37735	+	2.10159i	0.0758204	+	0.115689i
$331$	−6.92796	+	5.03346i	−0.380795	+	0.276664i	−0.761673	−	0.647961i	$-0.775622\pi$
$331$	−6.92796	+	5.03346i	−0.380795	+	0.276664i	0.380878	+	0.924625i	$0.375622\pi$
$332$	−12.3356			−0.677004
$333$	6.99359	−	5.08114i	0.383246	−	0.278445i
$334$	−2.52039	−	7.75696i	−0.137910	−	0.424442i
$335$	2.09972	−	2.61528i	0.114720	−	0.142888i
$336$	0.347249	−	1.06872i	0.0189440	−	0.0583036i
$337$	−4.53365	−	13.9531i	−0.246964	−	0.760076i	−0.995307	−	0.0967646i	$-0.969151\pi$
$337$	−4.53365	−	13.9531i	−0.246964	−	0.760076i	0.748344	−	0.663311i	$-0.230849\pi$
$338$	2.41892	+	7.44466i	0.131572	+	0.404936i
$339$	−0.725760	+	2.23366i	−0.0394179	+	0.121316i
$340$	−11.7610	+	3.20425i	−0.637831	+	0.173775i
$341$	1.54574	+	4.75731i	0.0837068	+	0.257623i
$342$	−8.27383	+	6.01129i	−0.447398	+	0.325053i
$343$	11.0883			0.598715
$344$	1.32579	−	0.963245i	0.0714820	−	0.0519347i
$345$	−6.66378	+	8.29998i	−0.358766	+	0.446856i
$346$	2.02526	+	1.47144i	0.108879	+	0.0791049i
$347$	18.5970	+	13.5115i	0.998340	+	0.725337i	0.961732	−	0.273993i	$-0.0883445\pi$
$347$	18.5970	+	13.5115i	0.998340	+	0.725337i	0.0366088	+	0.999330i	$0.488344\pi$
$348$	−1.36239	+	4.19302i	−0.0730320	+	0.224769i
$349$	3.55023			0.190040			0.0950198	−	0.995475i	$-0.469709\pi$
$349$	3.55023			0.190040			0.0950198	+	0.995475i	$0.469709\pi$
$350$	0.900470	+	4.06837i	0.0481321	+	0.217463i
$351$	25.7339			1.37357
$352$	0.257524	−	0.792578i	0.0137261	−	0.0422445i
$353$	4.56375	+	3.31576i	0.242904	+	0.176480i	0.702576	−	0.711609i	$-0.252033\pi$
$353$	4.56375	+	3.31576i	0.242904	+	0.176480i	−0.459672	+	0.888089i	$0.652033\pi$
$354$	14.7625	+	10.7256i	0.784618	+	0.570058i
$355$	−4.93707	−	1.87146i	−0.262033	−	0.0993267i
$356$	5.66780	−	4.11790i	0.300393	−	0.218248i
$357$	6.12586			0.324215
$358$	16.2067	−	11.7749i	0.856552	−	0.622322i
$359$	−5.22442	−	16.0791i	−0.275734	−	0.848623i	−0.989024	−	0.147754i	$-0.952796\pi$
$359$	−5.22442	−	16.0791i	−0.275734	−	0.848623i	0.713290	−	0.700869i	$-0.247204\pi$
$360$	−2.47097	−	0.936652i	−0.130232	−	0.0493659i
$361$	17.2710	−	53.1548i	0.909002	−	2.79762i
$362$	2.43453	+	7.49270i	0.127956	+	0.393808i
$363$	4.29413	+	13.2160i	0.225383	+	0.693658i
$364$	−1.17527	+	3.61712i	−0.0616011	+	0.189589i
$365$	0.358528	−	7.43749i	0.0187662	−	0.389296i
$366$	−2.45184	−	7.54600i	−0.128160	−	0.394436i
$367$	10.2044	−	7.41393i	0.532665	−	0.387004i	−0.288688	−	0.957423i	$-0.593219\pi$
$367$	10.2044	−	7.41393i	0.532665	−	0.387004i	0.821354	+	0.570419i	$0.193219\pi$
$368$	3.53019			0.184024
$369$	1.78492	−	1.29682i	0.0929193	−	0.0675099i
$370$	−15.7813	+	4.29957i	−0.820431	+	0.223524i
$371$	4.33327	+	3.14830i	0.224972	+	0.163452i
$372$	6.54788	+	4.75731i	0.339492	+	0.246655i
$373$	4.09435	−	12.6011i	0.211997	−	0.652460i	−0.787356	−	0.616499i	$-0.788551\pi$
$373$	4.09435	−	12.6011i	0.211997	−	0.652460i	0.999353	−	0.0359616i	$-0.0114494\pi$
$374$	4.54301			0.234913
$375$	−14.8593	+	2.54541i	−0.767330	+	0.131445i
$376$	−0.833366			−0.0429776
$377$	4.61106	−	14.1914i	0.237482	−	0.730894i
$378$	3.80170	+	2.76210i	0.195538	+	0.142067i
$379$	−18.0702	−	13.1288i	−0.928203	−	0.674379i	0.0173488	−	0.999849i	$-0.494477\pi$
$379$	−18.0702	−	13.1288i	−0.928203	−	0.674379i	−0.945552	+	0.325470i	$0.894477\pi$
$380$	18.6702	−	5.08664i	0.957762	−	0.260939i
$381$	6.18178	−	4.49133i	0.316702	−	0.230098i
$382$	−5.27521			−0.269903
$383$	−19.7019	+	14.3143i	−1.00672	+	0.731425i	−0.963519	−	0.267642i	$-0.913756\pi$
$383$	−19.7019	+	14.3143i	−1.00672	+	0.731425i	−0.0432012	+	0.999066i	$0.513756\pi$
$384$	−0.416683	−	1.28242i	−0.0212638	−	0.0654431i
$385$	0.0747738	−	1.55114i	0.00381082	−	0.0790536i
$386$	−4.15508	+	12.7880i	−0.211488	+	0.650893i
$387$	0.598463	+	1.84188i	0.0304216	+	0.0936279i
$388$	3.42705	+	10.5474i	0.173982	+	0.535462i
$389$	9.30500	−	28.6378i	0.471782	−	1.45200i	−0.378467	−	0.925615i	$-0.623548\pi$
$389$	9.30500	−	28.6378i	0.471782	−	1.45200i	0.850249	−	0.526381i	$-0.176452\pi$
$390$	−12.8670	−	4.87738i	−0.651544	−	0.246976i
$391$	5.94688	+	18.3026i	0.300746	+	0.925602i
$392$	5.10126	−	3.70628i	0.257652	−	0.187195i
$393$	22.2144			1.12057
$394$	4.39991	−	3.19672i	0.221664	−	0.161048i
$395$	10.8077	+	4.09681i	0.543796	+	0.206133i
$396$	0.796764	+	0.578883i	0.0400389	+	0.0290900i
$397$	−28.6152	−	20.7902i	−1.43616	−	1.04343i	−0.988828	−	0.149059i	$-0.952376\pi$
$397$	−28.6152	−	20.7902i	−1.43616	−	1.04343i	−0.447328	−	0.894370i	$-0.647624\pi$
$398$	−5.37968	+	16.5569i	−0.269659	+	0.829924i
$399$	−9.72459			−0.486839
$400$	3.74364	+	3.31439i	0.187182	+	0.165719i
$401$	−5.66794			−0.283043			−0.141522	−	0.989935i	$-0.545199\pi$
$401$	−5.66794			−0.283043			−0.141522	+	0.989935i	$0.545199\pi$
$402$	−0.624984	+	1.92350i	−0.0311714	+	0.0959356i
$403$	−22.1615	−	16.1013i	−1.10394	−	0.802061i
$404$	−10.2814	−	7.46988i	−0.511519	−	0.371640i
$405$	−5.68090	+	7.07577i	−0.282286	+	0.351598i
$406$	2.20440	−	1.60159i	0.109403	−	0.0794856i
$407$	6.09595			0.302165
$408$	5.94688	−	4.32066i	0.294414	−	0.213904i
$409$	5.98493	+	18.4197i	0.295936	+	0.910797i	0.982906	+	0.184111i	$0.0589405\pi$
$409$	5.98493	+	18.4197i	0.295936	+	0.910797i	−0.686970	+	0.726686i	$0.741060\pi$
$410$	−4.02775	+	1.09735i	−0.198916	+	0.0541941i
$411$	1.20557	−	3.71035i	0.0594662	−	0.183018i
$412$	2.16780	+	6.67180i	0.106800	+	0.328696i
$413$	−3.48495	−	10.7256i	−0.171483	−	0.527771i
$414$	−1.28919	+	3.96772i	−0.0633603	+	0.195003i
$415$	−17.2687	+	21.5088i	−0.847687	+	1.05582i
$416$	1.41027	+	4.34038i	0.0691444	+	0.212805i
$417$	5.44301	−	3.95458i	0.266545	−	0.193657i
$418$	−7.21188			−0.352744
$419$	−18.5906	+	13.5068i	−0.908209	+	0.659853i	−0.940561	−	0.339624i	$-0.889700\pi$
$419$	−18.5906	+	13.5068i	−0.908209	+	0.659853i	0.0323520	+	0.999477i	$0.489700\pi$
$420$	−1.37735	−	2.10159i	−0.0672076	−	0.102547i
$421$	8.19306	+	5.95261i	0.399305	+	0.290112i	0.769258	−	0.638938i	$-0.220626\pi$
$421$	8.19306	+	5.95261i	0.399305	+	0.290112i	−0.369953	+	0.929051i	$0.620626\pi$
$422$	0.218381	+	0.158663i	0.0106306	+	0.00772361i
$423$	0.304337	−	0.936652i	0.0147974	−	0.0455416i
$424$	6.42721			0.312133
$425$	−10.8773	+	24.9926i	−0.527626	+	1.21232i
$426$	3.18392			0.154261
$427$	−1.51532	+	4.66369i	−0.0733316	+	0.225692i
$428$	8.71314	+	6.33047i	0.421165	+	0.305995i
$429$	4.14895	+	3.01439i	0.200313	+	0.145536i
$430$	0.176440	−	3.66015i	0.00850867	−	0.176508i
$431$	23.0589	−	16.7533i	1.11071	−	0.806978i	0.127935	−	0.991783i	$-0.459165\pi$
$431$	23.0589	−	16.7533i	1.11071	−	0.806978i	0.982775	+	0.184804i	$0.0591651\pi$
$432$	5.63877			0.271295
$433$	−12.8550	+	9.33971i	−0.617772	+	0.448838i	−0.852143	−	0.523309i	$-0.824697\pi$
$433$	−12.8550	+	9.33971i	−0.617772	+	0.448838i	0.234370	+	0.972147i	$0.424697\pi$
$434$	−1.54574	−	4.75731i	−0.0741981	−	0.228358i
$435$	5.40387	+	8.24535i	0.259096	+	0.395334i
$436$	−3.28655	+	10.1150i	−0.157397	+	0.484419i
$437$	−9.44047	−	29.0548i	−0.451599	−	1.38988i
$438$	1.38756	+	4.27046i	0.0663000	+	0.204051i
$439$	0.910550	−	2.80238i	0.0434582	−	0.133751i	−0.926973	−	0.375127i	$-0.877599\pi$
$439$	0.910550	−	2.80238i	0.0434582	−	0.133751i	0.970431	+	0.241377i	$0.0775990\pi$
$440$	−1.02146	−	1.55856i	−0.0486960	−	0.0743016i
$441$	2.30271	+	7.08700i	0.109653	+	0.337476i
$442$	−20.1274	+	14.6234i	−0.957362	+	0.695564i
$443$	−5.27327			−0.250541			−0.125270	−	0.992123i	$-0.539980\pi$
$443$	−5.27327			−0.250541			−0.125270	+	0.992123i	$0.539980\pi$
$444$	7.97971	−	5.79760i	0.378700	−	0.275142i
$445$	0.754284	−	15.6472i	0.0357565	−	0.741750i
$446$	−18.7460	−	13.6197i	−0.887647	−	0.644914i
$447$	2.18809	+	1.58974i	0.103493	+	0.0751922i
$448$	−0.257524	+	0.792578i	−0.0121669	+	0.0374458i
$449$	−6.81659			−0.321695			−0.160847	−	0.986979i	$-0.551423\pi$
$449$	−6.81659			−0.321695			−0.160847	+	0.986979i	$0.551423\pi$
$450$	−5.09231	+	2.99724i	−0.240054	+	0.141291i
$451$	1.55583			0.0732609
$452$	0.538232	−	1.65651i	0.0253163	−	0.0779156i
$453$	−2.14874	−	1.56115i	−0.100956	−	0.0733491i
$454$	0.204401	+	0.148506i	0.00959300	+	0.00696972i
$455$	4.66167	+	7.11289i	0.218542	+	0.333457i
$456$	−9.44047	+	6.85890i	−0.442090	+	0.321198i
$457$	4.17712			0.195397			0.0976987	−	0.995216i	$-0.468852\pi$
$457$	4.17712			0.195397			0.0976987	+	0.995216i	$0.468852\pi$
$458$	17.0625	−	12.3966i	0.797277	−	0.579255i
$459$	9.49893	+	29.2347i	0.443372	+	1.36456i
$460$	4.94194	−	6.15537i	0.230419	−	0.286995i
$461$	−11.5678	+	35.6020i	−0.538766	+	1.65815i	0.196601	+	0.980484i	$0.437010\pi$
$461$	−11.5678	+	35.6020i	−0.538766	+	1.65815i	−0.735367	+	0.677669i	$0.762990\pi$
$462$	0.289386	+	0.890637i	0.0134634	+	0.0414362i
$463$	−4.28879	−	13.1995i	−0.199317	−	0.613434i	−0.999899	−	0.0142111i	$-0.995476\pi$
$463$	−4.28879	−	13.1995i	−0.199317	−	0.613434i	0.800582	−	0.599223i	$-0.204524\pi$
$464$	1.01037	−	3.10959i	0.0469052	−	0.144359i
$465$	17.4614	−	4.75731i	0.809755	−	0.220615i
$466$	−4.51398	−	13.8926i	−0.209106	−	0.643562i
$467$	−11.2134	+	8.14705i	−0.518896	+	0.377000i	−0.816188	−	0.577786i	$-0.803917\pi$
$467$	−11.2134	+	8.14705i	−0.518896	+	0.377000i	0.297292	+	0.954787i	$0.403917\pi$
$468$	−5.39334			−0.249307
$469$	1.01125	−	0.734713i	0.0466950	−	0.0339259i
$470$	−1.16663	+	1.45309i	−0.0538128	+	0.0670258i
$471$	8.49222	+	6.16996i	0.391301	+	0.284297i
$472$	−10.9480	−	7.95422i	−0.503924	−	0.366123i
$473$	−0.422023	+	1.29885i	−0.0194046	+	0.0597213i
$474$	−6.96990			−0.320138
$475$	17.2673	−	39.6749i	0.792279	−	1.82041i
$476$	−4.54301			−0.208228
$477$	−2.34715	+	7.22379i	−0.107469	+	0.330755i
$478$	−4.70704	−	3.41986i	−0.215295	−	0.156421i
$479$	−23.2976	−	16.9267i	−1.06450	−	0.773401i	−0.0895806	−	0.995980i	$-0.528553\pi$
$479$	−23.2976	−	16.9267i	−1.06450	−	0.773401i	−0.974915	+	0.222578i	$0.928553\pi$
$480$	−2.81939	−	1.06872i	−0.128687	−	0.0487803i
$481$	−27.0076	+	19.6221i	−1.23144	+	0.894692i
$482$	13.7291			0.625345
$483$	−3.20933	+	2.33172i	−0.146030	+	0.106097i
$484$	−3.18458	−	9.80111i	−0.144753	−	0.445505i
$485$	23.1883	+	8.78982i	1.05293	+	0.399125i
$486$	−3.53650	+	10.8842i	−0.160419	+	0.493719i
$487$	12.0366	+	37.0449i	0.545430	+	1.67866i	0.719964	+	0.694011i	$0.244158\pi$
$487$	12.0366	+	37.0449i	0.545430	+	1.67866i	−0.174534	+	0.984651i	$0.555842\pi$
$488$	1.81832	+	5.59621i	0.0823114	+	0.253328i
$489$	−5.87354	+	18.0769i	−0.265611	+	0.817466i
$490$	0.678887	−	14.0832i	0.0306690	−	0.636213i
$491$	−7.26403	−	22.3564i	−0.327821	−	1.00893i	−0.970151	−	0.242501i	$-0.922032\pi$
$491$	−7.26403	−	22.3564i	−0.327821	−	1.00893i	0.642330	−	0.766428i	$-0.277968\pi$
$492$	2.03660	−	1.47968i	0.0918171	−	0.0667090i
$493$	17.8240			0.802753
$494$	31.9515	−	23.2141i	1.43757	−	1.04445i
$495$	2.12476	−	0.578883i	0.0955007	−	0.0260189i
$496$	−4.85599	−	3.52808i	−0.218040	−	0.158416i
$497$	−1.59196	−	1.15662i	−0.0714091	−	0.0518817i
$498$	5.14003	−	15.8194i	0.230330	−	0.708884i
$499$	28.2651			1.26532			0.632660	−	0.774430i	$-0.281963\pi$
$499$	28.2651			1.26532			0.632660	+	0.774430i	$0.281963\pi$
$500$	11.0198	−	1.88771i	0.492822	−	0.0844209i
$501$	10.9979			0.491348
$502$	−4.91144	+	15.1159i	−0.219208	+	0.674654i
$503$	−5.58565	−	4.05821i	−0.249052	−	0.180947i	0.456255	−	0.889849i	$-0.349191\pi$
$503$	−5.58565	−	4.05821i	−0.249052	−	0.180947i	−0.705306	+	0.708903i	$0.749191\pi$
$504$	−0.796764	−	0.578883i	−0.0354907	−	0.0257855i
$505$	−27.4178	+	7.46988i	−1.22007	+	0.332405i
$506$	−2.38008	+	1.72923i	−0.105808	+	0.0768737i
$507$	−10.5551			−0.468768
$508$	−4.58448	+	3.33082i	−0.203403	+	0.147781i
$509$	10.3641	+	31.8975i	0.459382	+	1.41383i	0.865913	+	0.500195i	$0.166738\pi$
$509$	10.3641	+	31.8975i	0.459382	+	1.41383i	−0.406531	+	0.913637i	$0.633262\pi$
$510$	0.791424	−	16.4177i	0.0350448	−	0.726988i
$511$	0.857557	−	2.63929i	0.0379361	−	0.116755i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−15.0792	−	46.4091i	−0.665765	−	2.04901i
$514$	−0.714612	+	2.19935i	−0.0315202	+	0.0970091i
$515$	14.6679	+	5.56005i	0.646345	+	0.245005i
$516$	0.682847	+	2.10159i	0.0300607	+	0.0925173i
$517$	0.561861	−	0.408216i	0.0247106	−	0.0179533i
$518$	−6.09595			−0.267841
$519$	−2.73089	+	1.98411i	−0.119873	+	0.0870926i
$520$	9.54229	+	3.61712i	0.418457	+	0.158621i
$521$	−0.997861	−	0.724989i	−0.0437171	−	0.0317623i	0.565712	−	0.824603i	$-0.308601\pi$
$521$	−0.997861	−	0.724989i	−0.0437171	−	0.0317623i	−0.609429	+	0.792840i	$0.708601\pi$
$522$	3.12602	+	2.27118i	0.136822	+	0.0994071i
$523$	7.11681	−	21.9033i	0.311196	−	0.957764i	−0.666095	−	0.745867i	$-0.732036\pi$
$523$	7.11681	−	21.9033i	0.311196	−	0.957764i	0.977292	−	0.211898i	$-0.0679643\pi$
$524$	−16.4745			−0.719690
$525$	−5.59256	−	0.540440i	−0.244079	−	0.0235868i
$526$	−21.4593			−0.935671
$527$	10.1114	−	31.1196i	0.440458	−	1.35559i
$528$	0.909110	+	0.660507i	0.0395639	+	0.0287449i
$529$	8.52520	+	6.19392i	0.370661	+	0.269301i
$530$	8.99749	−	11.2067i	0.390826	−	0.486788i
$531$	12.9382	−	9.40013i	0.561469	−	0.407931i
$532$	7.21188			0.312674
$533$	−6.89294	+	5.00801i	−0.298566	+	0.216921i
$534$	2.91919	+	8.98434i	0.126326	+	0.388791i
$535$	23.2356	−	6.33047i	1.00456	−	0.273690i
$536$	0.463496	−	1.42649i	0.0200200	−	0.0616151i
$537$	8.34725	+	25.6902i	0.360210	+	1.10861i
$538$	6.60877	+	20.3397i	0.284924	+	0.876907i
$539$	−1.62382	+	4.99760i	−0.0699428	+	0.215262i
$540$	7.89375	−	9.83195i	0.339693	−	0.423100i
$541$	−8.27238	−	25.4598i	−0.355657	−	1.09460i	−0.955627	−	0.294578i	$-0.904821\pi$
$541$	−8.27238	−	25.4598i	−0.355657	−	1.09460i	0.599970	−	0.800023i	$-0.295179\pi$
$542$	21.1400	−	15.3591i	0.908042	−	0.659731i
$543$	−10.6232			−0.455885
$544$	−4.41027	+	3.20425i	−0.189089	+	0.137381i
$545$	13.0359	+	19.8906i	0.558398	+	0.852018i
$546$	−4.14895	−	3.01439i	−0.177559	−	0.129004i
$547$	−5.19947	−	3.77763i	−0.222313	−	0.161520i	0.471054	−	0.882104i	$-0.343874\pi$
$547$	−5.19947	−	3.77763i	−0.222313	−	0.161520i	−0.693367	+	0.720584i	$0.743874\pi$
$548$	−0.894062	+	2.75164i	−0.0381924	+	0.117544i
$549$	−6.95383			−0.296782
$550$	−4.14751	−	0.400797i	−0.176850	−	0.0170900i
$551$	−28.2950			−1.20541
$552$	−1.47097	+	4.52718i	−0.0626087	+	0.192690i
$553$	3.48495	+	2.53197i	0.148195	+	0.107670i
$554$	15.0856	+	10.9604i	0.640928	+	0.465661i
$555$	1.06196	−	22.0298i	0.0450776	−	0.935113i
$556$	−4.03660	+	2.93276i	−0.171190	+	0.124377i
$557$	44.0843			1.86791			0.933957	−	0.357386i	$-0.116332\pi$
$557$	44.0843			1.86791			0.933957	+	0.357386i	$0.116332\pi$
$558$	5.73871	−	4.16941i	0.242939	−	0.176505i
$559$	−2.31112	−	7.11289i	−0.0977498	−	0.300843i
$560$	1.02146	+	1.55856i	0.0431644	+	0.0658613i
$561$	−1.89299	+	5.82604i	−0.0799223	+	0.245975i
$562$	4.57924	+	14.0934i	0.193164	+	0.594496i
$563$	6.20440	+	19.0952i	0.261484	+	0.804766i	0.992483	+	0.122387i	$0.0390548\pi$
$563$	6.20440	+	19.0952i	0.261484	+	0.804766i	−0.730998	+	0.682379i	$0.760945\pi$
$564$	0.347249	−	1.06872i	0.0146218	−	0.0450014i
$565$	−2.13487	−	3.25744i	−0.0898147	−	0.137041i
$566$	4.87628	+	15.0076i	0.204965	+	0.630818i
$567$	−2.73597	+	1.98780i	−0.114900	+	0.0834797i
$568$	−2.36123			−0.0990750
$569$	24.2170	−	17.5947i	1.01523	−	0.737609i	0.0499312	−	0.998753i	$-0.484100\pi$
$569$	24.2170	−	17.5947i	1.01523	−	0.737609i	0.965300	+	0.261144i	$0.0840998\pi$
$570$	−1.25636	+	26.0625i	−0.0526231	+	1.09164i
$571$	11.5201	+	8.36985i	0.482102	+	0.350267i	0.802139	−	0.597138i	$-0.203695\pi$
$571$	11.5201	+	8.36985i	0.482102	+	0.350267i	−0.320037	+	0.947405i	$0.603695\pi$
$572$	−3.07691	−	2.23551i	−0.128652	−	0.0934712i
$573$	2.19809	−	6.76503i	0.0918265	−	0.282613i
$574$	−1.55583			−0.0649389
$575$	−3.81445	−	17.2339i	−0.159074	−	0.718703i
$576$	−1.18178			−0.0492408
$577$	−5.62687	+	17.3177i	−0.234250	+	0.720946i	0.762970	+	0.646433i	$0.223740\pi$
$577$	−5.62687	+	17.3177i	−0.234250	+	0.720946i	−0.997220	+	0.0745128i	$0.976260\pi$
$578$	−10.2889	−	7.47531i	−0.427961	−	0.310932i
$579$	−14.6682	−	10.6571i	−0.609591	−	0.442894i
$580$	−4.00757	−	6.11485i	−0.166405	−	0.253905i
$581$	−8.31675	+	6.04247i	−0.345037	+	0.250684i
$582$	−14.9541			−0.619869
$583$	−4.33327	+	3.14830i	−0.179466	+	0.130389i
$584$	−1.02903	−	3.16703i	−0.0425815	−	0.131052i
$585$	−7.55018	+	9.40402i	−0.312161	+	0.388808i
$586$	5.68601	−	17.4998i	0.234887	−	0.722908i
$587$	1.59586	+	4.91155i	0.0658681	+	0.202721i	0.978574	−	0.205896i	$-0.0660110\pi$
$587$	1.59586	+	4.91155i	0.0658681	+	0.202721i	−0.912706	+	0.408618i	$0.866011\pi$
$588$	2.62739	+	8.08629i	0.108352	+	0.333473i
$589$	−16.0515	+	49.4014i	−0.661389	+	2.03555i
$590$	−29.1955	+	7.95422i	−1.20196	+	0.327470i
$591$	2.26616	+	6.97454i	0.0932176	+	0.286894i
$592$	−5.91785	+	4.29957i	−0.243222	+	0.176711i
$593$	−35.6286			−1.46309			−0.731546	−	0.681793i	$-0.761201\pi$
$593$	−35.6286			−1.46309			−0.731546	+	0.681793i	$0.761201\pi$
$594$	−3.80170	+	2.76210i	−0.155986	+	0.113330i
$595$	−6.35979	+	7.92135i	−0.260726	+	0.324744i
$596$	−1.62271	−	1.17897i	−0.0664690	−	0.0482925i
$597$	−18.9913	−	13.7980i	−0.777262	−	0.564714i
$598$	4.97854	−	15.3224i	0.203588	−	0.626579i
$599$	−31.8284			−1.30047			−0.650236	−	0.759733i	$-0.725330\pi$
$599$	−31.8284			−1.30047			−0.650236	+	0.759733i	$0.725330\pi$
$600$	−5.81034	+	3.41986i	−0.237206	+	0.139615i
$601$	−12.6378			−0.515508			−0.257754	−	0.966211i	$-0.582982\pi$
$601$	−12.6378			−0.515508			−0.257754	+	0.966211i	$0.582982\pi$
$602$	0.422023	−	1.29885i	0.0172004	−	0.0529373i
$603$	1.43403	+	1.04188i	0.0583981	+	0.0424287i
$604$	1.59353	+	1.15777i	0.0648397	+	0.0471088i
$605$	−21.5477	−	8.16791i	−0.876037	−	0.332073i
$606$	13.8636	−	10.0725i	0.563170	−	0.409167i
$607$	34.9481			1.41850			0.709250	−	0.704957i	$-0.249034\pi$
$607$	34.9481			1.41850			0.709250	+	0.704957i	$0.249034\pi$
$608$	7.00116	−	5.08664i	0.283935	−	0.206291i
$609$	1.13537	+	3.49432i	0.0460076	+	0.141597i
$610$	12.3032	+	4.66369i	0.498142	+	0.188827i
$611$	−1.17527	+	3.61712i	−0.0475465	+	0.146333i
$612$	−1.99080	−	6.12704i	−0.0804732	−	0.247671i
$613$	2.20106	+	6.77418i	0.0889001	+	0.273606i	0.985616	−	0.169000i	$-0.0540538\pi$
$613$	2.20106	+	6.77418i	0.0889001	+	0.273606i	−0.896716	+	0.442607i	$0.854054\pi$
$614$	−10.5430	+	32.4480i	−0.425481	+	1.30950i
$615$	0.271036	−	5.62250i	0.0109292	−	0.226721i
$616$	−0.214612	−	0.660507i	−0.00864696	−	0.0266126i
$617$	13.0147	−	9.45572i	0.523951	−	0.380673i	−0.294139	−	0.955763i	$-0.595033\pi$
$617$	13.0147	−	9.45572i	0.523951	−	0.380673i	0.818090	+	0.575090i	$0.195033\pi$
$618$	−9.45932			−0.380510
$619$	0.607103	−	0.441086i	0.0244015	−	0.0177287i	−0.575518	−	0.817789i	$-0.695199\pi$
$619$	0.607103	−	0.441086i	0.0244015	−	0.0177287i	0.599919	+	0.800061i	$0.295199\pi$
$620$	−12.9496	+	3.52808i	−0.520069	+	0.141691i
$621$	−16.1043	−	11.7004i	−0.646241	−	0.469522i
$622$	10.5479	+	7.66348i	0.422931	+	0.307278i
$623$	1.80416	−	5.55263i	0.0722821	−	0.222461i
$624$	−6.15382			−0.246350
$625$	12.1353	−	21.8572i	0.485410	−	0.874287i
$626$	3.48262			0.139194
$627$	3.00507	−	9.24864i	0.120011	−	0.369355i
$628$	−6.29793	−	4.57571i	−0.251315	−	0.182591i
$629$	−32.2606	−	23.4387i	−1.28631	−	0.934561i
$630$	−2.12476	+	0.578883i	−0.0846523	+	0.0230633i
$631$	12.4391	−	9.03753i	0.495192	−	0.359778i	−0.311985	−	0.950087i	$-0.600994\pi$
$631$	12.4391	−	9.03753i	0.495192	−	0.359778i	0.807178	+	0.590309i	$0.200994\pi$
$632$	5.16896			0.205610
$633$	−0.294468	+	0.213944i	−0.0117041	+	0.00850350i
$634$	1.48957	+	4.58443i	0.0591585	+	0.182071i
$635$	−0.610113	+	12.6565i	−0.0242116	+	0.502258i
$636$	−2.67811	+	8.24237i	−0.106194	+	0.326831i
$637$	−8.89249	−	27.3683i	−0.352333	−	1.08437i
$638$	0.842006	+	2.59143i	0.0333353	+	0.102596i
$639$	0.862297	−	2.65388i	0.0341120	−	0.104986i
$640$	2.09089	+	0.792578i	0.0826497	+	0.0313294i
$641$	2.92140	+	8.99114i	0.115388	+	0.355129i	0.992028	−	0.126019i	$-0.0402200\pi$
$641$	2.92140	+	8.99114i	0.115388	+	0.355129i	−0.876639	+	0.481148i	$0.840220\pi$
$642$	−11.7489	+	8.53609i	−0.463693	+	0.336893i
$643$	32.8334			1.29482			0.647411	−	0.762141i	$-0.275852\pi$
$643$	32.8334			1.29482			0.647411	+	0.762141i	$0.275852\pi$
$644$	2.38008	−	1.72923i	0.0937883	−	0.0681412i
$645$	4.62032	+	1.75139i	0.181925	+	0.0689610i
$646$	38.1661	+	27.7293i	1.50163	+	1.09100i
$647$	−14.4556	−	10.5026i	−0.568309	−	0.412901i	0.266182	−	0.963923i	$-0.414238\pi$
$647$	−14.4556	−	10.5026i	−0.568309	−	0.412901i	−0.834490	+	0.551022i	$0.814238\pi$
$648$	−1.25401	+	3.85944i	−0.0492621	+	0.151613i
$649$	11.2775			0.442682
$650$	19.6653	−	11.5746i	0.771335	−	0.453994i
$651$	6.74495			0.264355
$652$	4.35589	−	13.4060i	0.170590	−	0.525021i
$653$	25.8596	+	18.7881i	1.01196	+	0.735235i	0.964620	−	0.263644i	$-0.0849245\pi$
$653$	25.8596	+	18.7881i	1.01196	+	0.735235i	0.0473435	+	0.998879i	$0.484924\pi$
$654$	−11.6022	−	8.42947i	−0.453681	−	0.329618i
$655$	−23.0627	+	28.7254i	−0.901135	+	1.12240i
$656$	−1.51037	+	1.09735i	−0.0589700	+	0.0428442i
$657$	3.93534			0.153532
$658$	−0.561861	+	0.408216i	−0.0219036	+	0.0159139i
$659$	−3.52244	−	10.8410i	−0.137215	−	0.422304i	0.858713	−	0.512457i	$-0.171264\pi$
$659$	−3.52244	−	10.8410i	−0.137215	−	0.422304i	−0.995928	+	0.0901527i	$0.971264\pi$
$660$	2.42435	−	0.660507i	0.0943678	−	0.0257102i
$661$	2.26642	−	6.97531i	0.0881533	−	0.271308i	−0.897256	−	0.441511i	$-0.854442\pi$
$661$	2.26642	−	6.97531i	0.0881533	−	0.271308i	0.985409	+	0.170203i	$0.0544425\pi$
$662$	2.64625	+	8.14431i	0.102849	+	0.316537i
$663$	−10.3666	−	31.9050i	−0.402604	−	1.23909i
$664$	−3.81191	+	11.7319i	−0.147931	+	0.455284i
$665$	10.0960	−	12.5749i	0.391504	−	0.487633i
$666$	−2.67131	−	8.22146i	−0.103511	−	0.318575i
$667$	−9.33799	+	6.78445i	−0.361568	+	0.262695i
$668$	−8.15615			−0.315571
$669$	25.2773	−	18.3651i	0.977278	−	0.710034i
$670$	−1.83843	−	2.80512i	−0.0710248	−	0.108371i
$671$	−3.96717	−	2.88232i	−0.153151	−	0.111271i
$672$	−0.909110	−	0.660507i	−0.0350697	−	0.0254796i
$673$	−10.1243	+	31.1595i	−0.390264	+	1.20111i	0.542325	+	0.840169i	$0.317544\pi$
$673$	−10.1243	+	31.1595i	−0.390264	+	1.20111i	−0.932589	+	0.360940i	$0.882456\pi$
$674$	−14.6712			−0.565113
$675$	−6.09281	−	27.5276i	−0.234513	−	1.05954i
$676$	7.82777			0.301068
$677$	−10.0686	+	30.9879i	−0.386967	+	1.19096i	0.548076	+	0.836428i	$0.315360\pi$
$677$	−10.0686	+	30.9879i	−0.386967	+	1.19096i	−0.935043	+	0.354534i	$0.884640\pi$
$678$	1.90006	+	1.38048i	0.0729715	+	0.0530169i
$679$	7.47707	+	5.43241i	0.286944	+	0.208477i
$680$	−0.586930	+	12.1756i	−0.0225077	+	0.466911i
$681$	−0.275617	+	0.200247i	−0.0105617	+	0.00767349i
$682$	5.00214			0.191542
$683$	3.51875	−	2.55652i	0.134641	−	0.0978227i	−0.518426	−	0.855123i	$-0.673482\pi$
$683$	3.51875	−	2.55652i	0.134641	−	0.0978227i	0.653067	+	0.757300i	$0.273482\pi$
$684$	3.16032	+	9.72648i	0.120838	+	0.371901i
$685$	3.54625	+	5.41096i	0.135495	+	0.206742i
$686$	3.42649	−	10.5456i	0.130824	−	0.402635i
$687$	8.78799	+	27.0467i	0.335283	+	1.03189i
$688$	−0.506408	−	1.55856i	−0.0193066	−	0.0594197i
$689$	9.06413	−	27.8965i	0.345316	−	1.06277i
$690$	5.83453	+	8.90247i	0.222117	+	0.338911i
$691$	−6.26053	−	19.2679i	−0.238162	−	0.732987i	−0.996686	−	0.0813423i	$-0.974079\pi$
$691$	−6.26053	−	19.2679i	−0.238162	−	0.732987i	0.758524	−	0.651645i	$-0.225921\pi$
$692$	2.02526	−	1.47144i	0.0769888	−	0.0559356i
$693$	0.820744			0.0311775
$694$	18.5970	−	13.5115i	0.705933	−	0.512891i
$695$	−0.537200	+	11.1440i	−0.0203772	+	0.422714i
$696$	3.56680	+	2.59143i	0.135199	+	0.0982278i
$697$	−8.23362	−	5.98208i	−0.311871	−	0.226587i
$698$	1.09708	−	3.37647i	0.0415252	−	0.127801i
$699$	19.6970			0.745010
$700$	4.14751	+	0.400797i	0.156761	+	0.0151487i
$701$	12.5964			0.475758			0.237879	−	0.971295i	$-0.423548\pi$
$701$	12.5964			0.475758			0.237879	+	0.971295i	$0.423548\pi$
$702$	7.95222	−	24.4744i	0.300137	−	0.923727i
$703$	51.2126	+	37.2081i	1.93152	+	1.40333i
$704$	−0.674207	−	0.489840i	−0.0254101	−	0.0184615i
$705$	−1.37735	−	2.10159i	−0.0518738	−	0.0791504i
$706$	4.56375	−	3.31576i	0.171759	−	0.124790i
$707$	−10.5908			−0.398310
$708$	14.7625	−	10.7256i	0.554808	−	0.403092i
$709$	9.10924	+	28.0354i	0.342105	+	1.05289i	0.963116	+	0.269088i	$0.0867222\pi$
$709$	9.10924	+	28.0354i	0.342105	+	1.05289i	−0.621011	+	0.783802i	$0.713278\pi$
$710$	−3.30550	+	4.11712i	−0.124053	+	0.154513i
$711$	−1.88765	+	5.80960i	−0.0707926	+	0.217877i
$712$	−2.16491	−	6.66290i	−0.0811333	−	0.249703i
$713$	6.54788	+	20.1523i	0.245220	+	0.754710i
$714$	1.89299	−	5.82604i	0.0708435	−	0.218034i
$715$	−8.20529	+	2.23551i	−0.306860	+	0.0836032i
$716$	−6.19042	−	19.0522i	−0.231347	−	0.712012i
$717$	6.34704	−	4.61139i	0.237034	−	0.172216i
$718$	−16.9066			−0.630948
$719$	24.3987	−	17.7267i	0.909919	−	0.661095i	−0.0310756	−	0.999517i	$-0.509893\pi$
$719$	24.3987	−	17.7267i	0.909919	−	0.661095i	0.940994	+	0.338422i	$0.109893\pi$
$720$	−1.65438	+	2.06059i	−0.0616552	+	0.0767937i
$721$	4.72966	+	3.43630i	0.176142	+	0.127974i
$722$	−45.2162	−	32.8515i	−1.68277	−	1.22261i
$723$	−5.72069	+	17.6065i	−0.212755	+	0.654792i
$724$	7.87829			0.292794
$725$	−16.2723	−	1.57248i	−0.604338	−	0.0584006i
$726$	13.8961			0.515732
$727$	1.83783	−	5.65626i	0.0681614	−	0.209779i	−0.911174	−	0.412021i	$-0.864823\pi$
$727$	1.83783	−	5.65626i	0.0681614	−	0.209779i	0.979336	+	0.202242i	$0.0648229\pi$
$728$	3.07691	+	2.23551i	0.114038	+	0.0828533i
$729$	−22.3337	−	16.2264i	−0.827173	−	0.600976i
$730$	−6.96268	−	2.63929i	−0.257700	−	0.0976845i
$731$	7.22743	−	5.25103i	0.267316	−	0.194216i
$732$	−7.93434			−0.293261
$733$	−8.23281	+	5.98148i	−0.304086	+	0.220931i	−0.729355	−	0.684136i	$-0.760180\pi$
$733$	−8.23281	+	5.98148i	−0.304086	+	0.220931i	0.425269	+	0.905067i	$0.360180\pi$
$734$	−3.89773	−	11.9960i	−0.143868	−	0.442780i
$735$	17.7776	+	6.73884i	0.655738	+	0.248566i
$736$	1.09089	−	3.35741i	0.0402107	−	0.123756i
$737$	0.386261	+	1.18879i	0.0142281	+	0.0437896i
$738$	−0.681780	−	2.09830i	−0.0250967	−	0.0772396i
$739$	11.2234	−	34.5422i	0.412861	−	1.27066i	−0.501289	−	0.865280i	$-0.667141\pi$
$739$	11.2234	−	34.5422i	0.412861	−	1.27066i	0.914150	−	0.405376i	$-0.132859\pi$
$740$	−0.787561	+	16.3376i	−0.0289513	+	0.600581i
$741$	16.4566	+	50.6482i	0.604548	+	1.86061i
$742$	4.33327	−	3.14830i	0.159079	−	0.115578i
$743$	2.84832			0.104495			0.0522473	−	0.998634i	$-0.483362\pi$
$743$	2.84832			0.104495			0.0522473	+	0.998634i	$0.483362\pi$
$744$	6.54788	−	4.75731i	0.240057	−	0.174412i
$745$	−4.32734	+	1.17897i	−0.158542	+	0.0431941i
$746$	−10.7191	−	7.78791i	−0.392455	−	0.285136i
$747$	−11.7938	−	8.56871i	−0.431513	−	0.313513i
$748$	1.40387	−	4.32066i	0.0513305	−	0.157979i
$749$	8.97537			0.327953
$750$	−2.17094	+	14.9186i	−0.0792715	+	0.544750i
$751$	−31.5502			−1.15128			−0.575641	−	0.817702i	$-0.695248\pi$
$751$	−31.5502			−1.15128			−0.575641	+	0.817702i	$0.695248\pi$
$752$	−0.257524	+	0.792578i	−0.00939094	+	0.0289023i
$753$	−17.3383	−	12.5970i	−0.631844	−	0.459062i
$754$	−12.0719	−	8.77076i	−0.439633	−	0.319412i
$755$	4.24951	−	1.15777i	0.154656	−	0.0421354i
$756$	3.80170	−	2.76210i	0.138266	−	0.100456i
$757$	−45.6446			−1.65898			−0.829491	−	0.558520i	$-0.811369\pi$
$757$	−45.6446			−1.65898			−0.829491	+	0.558520i	$0.811369\pi$
$758$	−18.0702	+	13.1288i	−0.656339	+	0.476858i
$759$	−1.22586	−	3.77280i	−0.0444958	−	0.136944i
$760$	0.931731	−	19.3283i	0.0337974	−	0.701111i
$761$	2.80550	−	8.63445i	0.101699	−	0.312998i	−0.887242	−	0.461304i	$-0.847382\pi$
$761$	2.80550	−	8.63445i	0.101699	−	0.312998i	0.988942	+	0.148305i	$0.0473818\pi$
$762$	−2.36123	−	7.26712i	−0.0855383	−	0.263260i
$763$	2.73890	+	8.42947i	0.0991549	+	0.305167i
$764$	−1.63013	+	5.01702i	−0.0589760	+	0.181510i
$765$	−13.4703	−	5.10607i	−0.487018	−	0.184610i
$766$	7.52545	+	23.1610i	0.271906	+	0.836840i
$767$	−49.9641	+	36.3010i	−1.80410	+	1.31075i
$768$	−1.34841			−0.0486567
$769$	20.5964	−	14.9641i	0.742724	−	0.539621i	−0.150839	−	0.988558i	$-0.548198\pi$
$769$	20.5964	−	14.9641i	0.742724	−	0.539621i	0.893563	+	0.448938i	$0.148198\pi$
$770$	−1.45212	−	0.550444i	−0.0523308	−	0.0198366i
$771$	−2.52272	−	1.83286i	−0.0908535	−	0.0660089i
$772$	10.8781	+	7.90343i	0.391513	+	0.284451i
$773$	5.30034	−	16.3128i	0.190640	−	0.586729i	−0.809360	−	0.587313i	$-0.800186\pi$
$773$	5.30034	−	16.3128i	0.190640	−	0.586729i	1.00000		0.000583568i	$0.000185756\pi$
$774$	1.93667			0.0696120
$775$	−11.9766	+	27.5184i	−0.430211	+	0.988489i
$776$	11.0902			0.398114
$777$	2.54008	−	7.81756i	0.0911249	−	0.280453i
$778$	−24.3608	−	17.6992i	−0.873377	−	0.634546i
$779$	13.0706	+	9.49635i	0.468303	+	0.340242i
$780$	−8.61477	+	10.7300i	−0.308458	+	0.384196i
$781$	1.59196	−	1.15662i	0.0569647	−	0.0413873i
$782$	19.2445			0.688182
$783$	−14.9156	+	10.8368i	−0.533038	+	0.387275i
$784$	−1.94851	−	5.99689i	−0.0695895	−	0.214175i
$785$	−16.7949	+	4.57571i	−0.599435	+	0.163314i
$786$	6.86463	−	21.1271i	0.244853	−	0.753580i
$787$	3.48351	+	10.7211i	0.124174	+	0.382168i	0.993750	−	0.111632i	$-0.0356077\pi$
$787$	3.48351	+	10.7211i	0.124174	+	0.382168i	−0.869576	+	0.493799i	$0.835608\pi$
$788$	−1.68061	−	5.17240i	−0.0598694	−	0.184259i
$789$	8.94173	−	27.5198i	0.318334	−	0.979731i
$790$	7.23607	−	9.01278i	0.257448	−	0.320660i
$791$	−0.448544	−	1.38048i	−0.0159484	−	0.0490841i
$792$	0.796764	−	0.578883i	0.0283118	−	0.0205697i
$793$	26.8540			0.953613
$794$	−28.6152	+	20.7902i	−1.01552	+	0.737816i
$795$	10.6226	+	16.2082i	0.376744	+	0.574845i
$796$	14.0842	+	10.2328i	0.499200	+	0.362690i
$797$	21.5775	+	15.6770i	0.764315	+	0.555307i	0.900231	−	0.435413i	$-0.143398\pi$
$797$	21.5775	+	15.6770i	0.764315	+	0.555307i	−0.135916	+	0.990720i	$0.543398\pi$
$798$	−3.00507	+	9.24864i	−0.106378	+	0.327398i
$799$	−4.54301			−0.160720
$800$	4.30902	−	2.53621i	0.152347	−	0.0896686i
$801$	8.27929			0.292534
$802$	−1.75149	+	5.39053i	−0.0618472	+	0.190346i
$803$	2.24511	+	1.63117i	0.0792284	+	0.0575628i
$804$	1.63623	+	1.18879i	0.0577053	+	0.0419254i
$805$	0.316747	−	6.57075i	0.0111639	−	0.231589i
$806$	−22.1615	+	16.1013i	−0.780605	+	0.567143i
$807$	−28.8378			−1.01514
$808$	−10.2814	+	7.46988i	−0.361699	+	0.262789i
$809$	3.39121	+	10.4371i	0.119229	+	0.366948i	0.992805	−	0.119738i	$-0.0382056\pi$
$809$	3.39121	+	10.4371i	0.119229	+	0.366948i	−0.873577	+	0.486686i	$0.838206\pi$
$810$	4.97396	+	7.58939i	0.174767	+	0.266664i
$811$	−3.04882	+	9.38329i	−0.107058	+	0.329492i	−0.990208	−	0.139599i	$-0.955419\pi$
$811$	−3.04882	+	9.38329i	−0.107058	+	0.329492i	0.883150	+	0.469091i	$0.155419\pi$
$812$	−0.842006	−	2.59143i	−0.0295486	−	0.0909413i
$813$	10.8881	+	33.5102i	0.381864	+	1.17526i
$814$	1.88375	−	5.79760i	0.0660255	−	0.203206i
$815$	−17.2774	−	26.3623i	−0.605201	−	0.923431i
$816$	−2.27150	−	6.99097i	−0.0795186	−	0.244733i
$817$	−11.4733	+	8.33584i	−0.401400	+	0.291634i
$818$	19.3676			0.677174
$819$	−3.63623	+	2.64187i	−0.127060	+	0.0923146i
$820$	−0.201003	+	4.16971i	−0.00701934	+	0.145613i
$821$	1.85904	+	1.35067i	0.0648808	+	0.0471387i	0.619753	−	0.784797i	$-0.287233\pi$
$821$	1.85904	+	1.35067i	0.0648808	+	0.0471387i	−0.554872	+	0.831936i	$0.687233\pi$
$822$	−3.15621	−	2.29312i	−0.110086	−	0.0799818i
$823$	0.248884	−	0.765985i	0.00867554	−	0.0267006i	−0.946625	−	0.322337i	$-0.895532\pi$
$823$	0.248884	−	0.765985i	0.00867554	−	0.0267006i	0.955301	+	0.295636i	$0.0955316\pi$
$824$	7.01515			0.244384
$825$	2.24218	−	5.15183i	0.0780629	−	0.179364i
$826$	−11.2775			−0.392396
$827$	11.2650	−	34.6701i	0.391722	−	1.20560i	−0.539762	−	0.841817i	$-0.681486\pi$
$827$	11.2650	−	34.6701i	0.391722	−	1.20560i	0.931485	−	0.363780i	$-0.118514\pi$
$828$	3.37515	+	2.45219i	0.117294	+	0.0852194i
$829$	−23.9231	−	17.3811i	−0.830883	−	0.603672i	0.0889263	−	0.996038i	$-0.471656\pi$
$829$	−23.9231	−	17.3811i	−0.830883	−	0.603672i	−0.919809	+	0.392367i	$0.871656\pi$
$830$	15.1197	+	23.0701i	0.524814	+	0.800774i
$831$	−20.3417	+	14.7791i	−0.705646	+	0.512682i
$832$	4.56375			0.158219
$833$	27.8090	−	20.2044i	0.963525	−	0.700042i
$834$	−2.07904	−	6.39864i	−0.0719914	−	0.221567i
$835$	−11.4178	+	14.2213i	−0.395131	+	0.492150i
$836$	−2.22859	+	6.85890i	−0.0770775	+	0.237220i
$837$	10.4589	+	32.1892i	0.361513	+	1.11262i
$838$	7.10097	+	21.8545i	0.245299	+	0.754953i
$839$	−13.4507	+	41.3969i	−0.464369	+	1.42918i	0.395405	+	0.918507i	$0.370604\pi$
$839$	−13.4507	+	41.3969i	−0.464369	+	1.42918i	−0.859774	+	0.510674i	$0.829396\pi$
$840$	−2.42435	+	0.660507i	−0.0836481	+	0.0227897i
$841$	−5.65797	−	17.4135i	−0.195103	−	0.600464i
$842$	8.19306	−	5.95261i	0.282351	−	0.205140i
$843$	−19.9818			−0.688209
$844$	0.218381	−	0.158663i	0.00751699	−	0.00546141i
$845$	10.9582	−	13.6488i	0.376972	−	0.469532i
$846$	−0.796764	−	0.578883i	−0.0273933	−	0.0199024i
$847$	−6.94804	−	5.04805i	−0.238738	−	0.173453i
$848$	1.98612	−	6.11264i	0.0682035	−	0.209909i
$849$	−21.2779			−0.730257
$850$	20.4081	+	18.0680i	0.699991	+	0.619729i
$851$	25.8229			0.885197
$852$	0.983884	−	3.02808i	0.0337073	−	0.103740i
$853$	−40.9415	−	29.7458i	−1.40181	−	1.01848i	−0.994450	−	0.105208i	$-0.966449\pi$
$853$	−40.9415	−	29.7458i	−1.40181	−	1.01848i	−0.407361	−	0.913267i	$-0.633551\pi$
$854$	3.96717	+	2.88232i	0.135754	+	0.0986308i
$855$	21.3836	+	8.10571i	0.731303	+	0.277209i
$856$	8.71314	−	6.33047i	0.297809	−	0.216371i
$857$	34.1589			1.16684			0.583422	−	0.812169i	$-0.301713\pi$
$857$	34.1589			1.16684			0.583422	+	0.812169i	$0.301713\pi$
$858$	4.14895	−	3.01439i	0.141643	−	0.102909i
$859$	3.39523	+	10.4494i	0.115844	+	0.356530i	0.992122	−	0.125275i	$-0.0399813\pi$
$859$	3.39523	+	10.4494i	0.115844	+	0.356530i	−0.876278	+	0.481805i	$0.839981\pi$
$860$	−3.42649	−	1.29885i	−0.116842	−	0.0442905i
$861$	0.648286	−	1.99522i	0.0220935	−	0.0679968i
$862$	−8.80773	−	27.1074i	−0.299993	−	0.923282i
$863$	−14.3100	−	44.0415i	−0.487117	−	1.49919i	−0.828891	−	0.559410i	$-0.811028\pi$
$863$	−14.3100	−	44.0415i	−0.487117	−	1.49919i	0.341774	−	0.939782i	$-0.388972\pi$
$864$	1.74248	−	5.36279i	0.0592802	−	0.182446i
$865$	0.269526	−	5.59119i	0.00916417	−	0.190106i
$866$	4.91018	+	15.1120i	0.166855	+	0.513526i
$867$	13.8737	−	10.0798i	0.471175	−	0.342328i
$868$	−5.00214			−0.169784
$869$	−3.48495	+	2.53197i	−0.118219	+	0.0858911i
$870$	9.51168	−	2.59143i	0.322476	−	0.0878577i
$871$	−5.53786	−	4.02349i	−0.187643	−	0.136331i
$872$	8.60431	+	6.25140i	0.291379	+	0.211699i
$873$	−4.05002	+	12.4647i	−0.137072	+	0.421865i
$874$	−30.5500			−1.03337
$875$	6.50497	−	6.67066i	0.219908	−	0.225509i
$876$	4.49023			0.151711
$877$	6.48231	−	19.9505i	0.218892	−	0.673681i	−0.779962	−	0.625827i	$-0.784762\pi$
$877$	6.48231	−	19.9505i	0.218892	−	0.673681i	0.998854	−	0.0478541i	$-0.0152383\pi$
$878$	−2.38385	−	1.73197i	−0.0804511	−	0.0584511i
$879$	20.0727	+	14.5837i	0.677037	+	0.491896i
$880$	−1.79793	+	0.489840i	−0.0606082	+	0.0165125i
$881$	41.1491	−	29.8966i	1.38635	−	1.00724i	0.390094	−	0.920775i	$-0.372442\pi$
$881$	41.1491	−	29.8966i	1.38635	−	1.00724i	0.996255	−	0.0864666i	$-0.0275576\pi$
$882$	7.45171			0.250912
$883$	39.7141	−	28.8540i	1.33649	−	0.971014i	0.336920	−	0.941533i	$-0.390615\pi$
$883$	39.7141	−	28.8540i	1.33649	−	0.971014i	0.999565	−	0.0294804i	$-0.00938527\pi$
$884$	7.68797	+	23.6611i	0.258574	+	0.795810i
$885$	1.96463	−	40.7552i	0.0660402	−	1.36997i
$886$	−1.62953	+	5.01518i	−0.0547451	+	0.168488i
$887$	−11.4242	−	35.1599i	−0.383586	−	1.18056i	−0.937501	−	0.347982i	$-0.886867\pi$
$887$	−11.4242	−	35.1599i	−0.383586	−	1.18056i	0.553915	−	0.832573i	$-0.313133\pi$
$888$	−3.04798	−	9.38071i	−0.102283	−	0.314796i
$889$	−1.45932	+	4.49133i	−0.0489440	+	0.150634i
$890$	−14.6483	−	5.55263i	−0.491013	−	0.186125i
$891$	−1.04505	−	3.21633i	−0.0350104	−	0.107751i
$892$	−18.7460	+	13.6197i	−0.627662	+	0.456023i
$893$	7.21188			0.241336
$894$	2.18809	−	1.58974i	0.0731807	−	0.0531689i
$895$	−41.8860	−	15.8774i	−1.40009	−	0.530723i
$896$	0.674207	+	0.489840i	0.0225237	+	0.0163644i
$897$	17.5752	+	12.7691i	0.586820	+	0.426349i
$898$	−2.10644	+	6.48297i	−0.0702929	+	0.216339i
$899$	19.6253			0.654542
$900$	1.27694	+	5.76927i	0.0425646	+	0.192309i
$901$	35.0373			1.16726
$902$	0.480776	−	1.47968i	0.0160081	−	0.0492679i
$903$	1.48982	+	1.08242i	0.0495782	+	0.0360207i
$904$	−1.40911	−	1.02378i	−0.0468663	−	0.0340504i
$905$	11.0289	−	13.7369i	0.366612	−	0.456629i
$906$	−2.14874	+	1.56115i	−0.0713870	+	0.0518657i
$907$	44.9718			1.49326			0.746632	−	0.665237i	$-0.231670\pi$
$907$	44.9718			1.49326			0.746632	+	0.665237i	$0.231670\pi$
$908$	0.204401	−	0.148506i	0.00678327	−	0.00492834i
$909$	−4.64102	−	14.2836i	−0.153933	−	0.473757i
$910$	8.20529	−	2.23551i	0.272003	−	0.0741063i
$911$	−8.32785	+	25.6305i	−0.275914	+	0.849176i	0.713062	+	0.701101i	$0.247308\pi$
$911$	−8.32785	+	25.6305i	−0.275914	+	0.849176i	−0.988976	+	0.148075i	$0.952692\pi$
$912$	3.60594	+	11.0979i	0.119405	+	0.367489i
$913$	−3.17671	−	9.77692i	−0.105134	−	0.323569i
$914$	1.29080	−	3.97268i	0.0426959	−	0.131404i
$915$	−11.1073	+	13.8346i	−0.367197	+	0.457357i
$916$	−6.51728	−	20.0581i	−0.215337	−	0.662739i
$917$	−11.1072	+	8.06985i	−0.366792	+	0.266490i
$918$	30.7392			1.01454
$919$	−25.8087	+	18.7511i	−0.851350	+	0.618542i	−0.925518	−	0.378704i	$-0.876370\pi$
$919$	−25.8087	+	18.7511i	−0.851350	+	0.618542i	0.0741679	+	0.997246i	$0.476370\pi$
$920$	−4.32696	−	6.60218i	−0.142656	−	0.217667i
$921$	−37.2189	−	27.0411i	−1.22640	−	0.891034i
$922$	30.2849	+	22.0033i	0.997380	+	0.724639i
$923$	−3.32998	+	10.2486i	−0.109608	+	0.337338i
$924$	0.936471			0.0308076
$925$	27.3842	+	24.2443i	0.900387	+	0.797147i
$926$	−13.8788			−0.456086
$927$	−2.56186	+	7.88460i	−0.0841426	+	0.258964i
$928$	−2.64518	−	1.92183i	−0.0868322	−	0.0630873i
$929$	5.06070	+	3.67681i	0.166036	+	0.120632i	0.667700	−	0.744430i	$-0.267279\pi$
$929$	5.06070	+	3.67681i	0.166036	+	0.120632i	−0.501664	+	0.865062i	$0.667279\pi$
$930$	0.871407	−	18.0769i	0.0285746	−	0.592765i
$931$	−44.1459	+	32.0738i	−1.44682	+	1.05118i
$932$	−14.6075			−0.478486
$933$	−14.2229	+	10.3335i	−0.465637	+	0.338305i
$934$	4.28316	+	13.1822i	0.140149	+	0.431335i
$935$	−5.56837	−	8.49635i	−0.182105	−	0.277860i
$936$	−1.66663	+	5.12937i	−0.0544756	+	0.167659i
$937$	−9.55466	−	29.4062i	−0.312137	−	0.960660i	−0.976917	−	0.213620i	$-0.931475\pi$
$937$	−9.55466	−	29.4062i	−0.312137	−	0.960660i	0.664780	−	0.747040i	$-0.268525\pi$
$938$	−0.386261	−	1.18879i	−0.0126119	−	0.0388154i
$939$	−1.45115	+	4.46618i	−0.0473565	+	0.145748i
$940$	1.02146	+	1.55856i	0.0333162	+	0.0508347i
$941$	−7.92136	−	24.3794i	−0.258229	−	0.794747i	−0.993176	−	0.116623i	$-0.962793\pi$
$941$	−7.92136	−	24.3794i	−0.258229	−	0.794747i	0.734947	−	0.678124i	$-0.237207\pi$
$942$	8.49222	−	6.16996i	0.276691	−	0.201028i
$943$	6.59058			0.214619
$944$	−10.9480	+	7.95422i	−0.356328	+	0.258888i
$945$	0.505939	−	10.4954i	0.0164582	−	0.341417i
$946$	1.10487	+	0.802735i	0.0359224	+	0.0260992i
$947$	36.5775	+	26.5751i	1.18861	+	0.863575i	0.993117	−	0.117130i	$-0.0373696\pi$
$947$	36.5775	+	26.5751i	1.18861	+	0.863575i	0.195492	+	0.980705i	$0.437370\pi$
$948$	−2.15382	+	6.62877i	−0.0699528	+	0.215293i
$949$	−15.1973			−0.493325
$950$	−32.3972	−	28.6824i	−1.05110	−	0.930580i
$951$	−6.49984			−0.210772
$952$	−1.40387	+	4.32066i	−0.0454996	+	0.140033i
$953$	16.6690	+	12.1107i	0.539961	+	0.392304i	0.824070	−	0.566487i	$-0.191698\pi$
$953$	16.6690	+	12.1107i	0.539961	+	0.392304i	−0.284110	+	0.958792i	$0.591698\pi$
$954$	6.14492	+	4.46455i	0.198949	+	0.144545i
$955$	6.46583	+	9.86572i	0.209229	+	0.319247i
$956$	−4.70704	+	3.41986i	−0.152237	+	0.110606i
$957$	−3.67414			−0.118768
$958$	−23.2976	+	16.9267i	−0.752712	+	0.546877i
$959$	0.745080	+	2.29312i	0.0240599	+	0.0740488i
$960$	−1.88765	+	2.35114i	−0.0609238	+	0.0758827i
$961$	1.55373	−	4.78188i	0.0501202	−	0.154254i
$962$	10.3160	+	31.7493i	0.332600	+	1.02364i
$963$	3.93311	+	12.1049i	0.126743	+	0.390074i
$964$	4.24254	−	13.0572i	0.136643	−	0.420544i
$965$	29.0091	−	7.90343i	0.933835	−	0.254421i
$966$	1.22586	+	3.77280i	0.0394413	+	0.121388i
$967$	41.3373	−	30.0333i	1.32932	−	0.965806i	0.329553	−	0.944137i	$-0.393102\pi$
$967$	41.3373	−	30.0333i	1.32932	−	0.965806i	0.999765	−	0.0216692i	$-0.00689807\pi$
$968$	−10.3055			−0.331231
$969$	−51.4638	+	37.3906i	−1.65325	+	1.20116i
$970$	15.5252	−	19.3372i	0.498484	−	0.620880i
$971$	−11.8229	−	8.58982i	−0.379414	−	0.275661i	0.381690	−	0.924291i	$-0.375342\pi$
$971$	−11.8229	−	8.58982i	−0.379414	−	0.275661i	−0.761104	+	0.648630i	$0.775342\pi$
$972$	9.25869	+	6.72683i	0.296973	+	0.215763i
$973$	−1.28492	+	3.95458i	−0.0411927	+	0.126778i
$974$	38.9513			1.24808
$975$	6.64933	+	30.0420i	0.212949	+	0.962115i
$976$	5.88420			0.188349
$977$	−16.1479	+	49.6981i	−0.516616	+	1.58998i	0.263705	+	0.964603i	$0.415055\pi$
$977$	−16.1479	+	49.6981i	−0.516616	+	1.58998i	−0.780322	+	0.625379i	$0.784945\pi$
$978$	15.3771	+	11.1721i	0.491707	+	0.357246i
$979$	4.72335	+	3.43171i	0.150959	+	0.109678i
$980$	−13.1841	−	4.99760i	−0.421151	−	0.159643i
$981$	−10.1684	+	7.38777i	−0.324652	+	0.235873i
$982$	−23.5069			−0.750135
$983$	−23.9541	+	17.4037i	−0.764016	+	0.555090i	−0.900140	−	0.435602i	$-0.856536\pi$
$983$	−23.9541	+	17.4037i	−0.764016	+	0.555090i	0.136123	+	0.990692i	$0.456536\pi$
$984$	−0.777913	−	2.39417i	−0.0247989	−	0.0763233i
$985$	−11.3715	−	4.31050i	−0.362325	−	0.137344i
$986$	5.50792	−	16.9516i	0.175408	−	0.539850i
$987$	−0.289386	−	0.890637i	−0.00921124	−	0.0283493i
$988$	−12.2044	−	37.5613i	−0.388274	−	1.19498i
$989$	−1.78772	+	5.50203i	−0.0568461	+	0.174954i
$990$	0.106035	−	2.19965i	0.00337002	−	0.0699094i
$991$	4.59673	+	14.1473i	0.146020	+	0.449403i	0.997141	−	0.0755666i	$-0.0240765\pi$
$991$	4.59673	+	14.1473i	0.146020	+	0.449403i	−0.851121	+	0.524970i	$0.824077\pi$
$992$	−4.85599	+	3.52808i	−0.154178	+	0.112017i
$993$	−11.5471			−0.366435
$994$	−1.59196	+	1.15662i	−0.0504938	+	0.0366859i
$995$	37.5587	−	10.2328i	1.19069	−	0.324400i
$996$	−13.4568	−	9.77692i	−0.426394	−	0.309794i
$997$	24.8971	+	18.0888i	0.788500	+	0.572879i	0.907518	−	0.420013i	$-0.137974\pi$
$997$	24.8971	+	18.0888i	0.788500	+	0.572879i	−0.119018	+	0.992892i	$0.537974\pi$
$998$	8.73440	−	26.8817i	0.276483	−	0.850926i
$999$	41.2468			1.30499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.2.d.b.21.2	✓	8
3.2	odd	2		450.2.h.e.271.2		8
4.3	odd	2		400.2.u.d.321.1		8
5.2	odd	4		250.2.e.c.149.4		16
5.3	odd	4		250.2.e.c.149.1		16
5.4	even	2		250.2.d.d.101.1		8
25.6	even	5	inner	50.2.d.b.31.2	yes	8
25.8	odd	20		250.2.e.c.99.4		16
25.9	even	10		1250.2.a.f.1.3		4
25.12	odd	20		1250.2.b.e.1249.7		8
25.13	odd	20		1250.2.b.e.1249.2		8
25.16	even	5		1250.2.a.l.1.2		4
25.17	odd	20		250.2.e.c.99.1		16
25.19	even	10		250.2.d.d.151.1		8
75.56	odd	10		450.2.h.e.181.2		8
100.31	odd	10		400.2.u.d.81.1		8
100.59	odd	10		10000.2.a.x.1.2		4
100.91	odd	10		10000.2.a.t.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.2	✓	8	1.1	even	1	trivial
50.2.d.b.31.2	yes	8	25.6	even	5	inner
250.2.d.d.101.1		8	5.4	even	2
250.2.d.d.151.1		8	25.19	even	10
250.2.e.c.99.1		16	25.17	odd	20
250.2.e.c.99.4		16	25.8	odd	20
250.2.e.c.149.1		16	5.3	odd	4
250.2.e.c.149.4		16	5.2	odd	4
400.2.u.d.81.1		8	100.31	odd	10
400.2.u.d.321.1		8	4.3	odd	2
450.2.h.e.181.2		8	75.56	odd	10
450.2.h.e.271.2		8	3.2	odd	2
1250.2.a.f.1.3		4	25.9	even	10
1250.2.a.l.1.2		4	25.16	even	5
1250.2.b.e.1249.2		8	25.13	odd	20
1250.2.b.e.1249.7		8	25.12	odd	20
10000.2.a.t.1.3		4	100.91	odd	10
10000.2.a.x.1.2		4	100.59	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.09089 + 0.792578i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 + 0.587785i) q^{5} +(1.09089 - 0.792578i) q^{6} -0.833366 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.365190 - 1.12394i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.09089 + 0.792578i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 + 0.587785i) q^{5} +(1.09089 - 0.792578i) q^{6} -0.833366 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.365190 - 1.12394i) q^{9} +(-0.107666 + 2.23347i) q^{10} +(0.257524 - 0.792578i) q^{11} +(-0.416683 - 1.28242i) q^{12} +(1.41027 + 4.34038i) q^{13} +(-0.257524 + 0.792578i) q^{14} +(-2.81939 - 1.06872i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.41027 + 3.20425i) q^{17} -1.18178 q^{18} +(7.00116 - 5.08664i) q^{19} +(2.09089 + 0.792578i) q^{20} +(-0.909110 - 0.660507i) q^{21} +(-0.674207 - 0.489840i) q^{22} +(1.09089 - 3.35741i) q^{23} -1.34841 q^{24} +(4.30902 - 2.53621i) q^{25} +4.56375 q^{26} +(1.74248 - 5.36279i) q^{27} +(0.674207 + 0.489840i) q^{28} +(-2.64518 - 1.92183i) q^{29} +(-1.88765 + 2.35114i) q^{30} +(-4.85599 + 3.52808i) q^{31} +1.00000 q^{32} +(0.909110 - 0.660507i) q^{33} +(1.68458 + 5.18459i) q^{34} +(1.79793 - 0.489840i) q^{35} +(-0.365190 + 1.12394i) q^{36} +(2.26042 + 6.95685i) q^{37} +(-2.67421 - 8.23036i) q^{38} +(-1.90163 + 5.85263i) q^{39} +(1.39991 - 1.74363i) q^{40} +(0.576909 + 1.77554i) q^{41} +(-0.909110 + 0.660507i) q^{42} -1.63877 q^{43} +(-0.674207 + 0.489840i) q^{44} +(1.44851 + 2.21017i) q^{45} +(-2.85599 - 2.07500i) q^{46} +(0.674207 + 0.489840i) q^{47} +(-0.416683 + 1.28242i) q^{48} -6.30550 q^{49} +(-1.08052 - 4.88185i) q^{50} -7.35074 q^{51} +(1.41027 - 4.34038i) q^{52} +(-5.19972 - 3.77782i) q^{53} +(-4.56186 - 3.31439i) q^{54} +(-0.0897250 + 1.86130i) q^{55} +(0.674207 - 0.489840i) q^{56} +11.6691 q^{57} +(-2.64518 + 1.92183i) q^{58} +(4.18178 + 12.8702i) q^{59} +(1.65275 + 2.52181i) q^{60} +(1.81832 - 5.59621i) q^{61} +(1.85482 + 5.70855i) q^{62} +(0.304337 + 0.936652i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-5.59378 - 8.53513i) q^{65} +(-0.347249 - 1.06872i) q^{66} +(-1.21345 + 0.881621i) q^{67} +5.45140 q^{68} +(3.85105 - 2.79795i) q^{69} +(0.0897250 - 1.86130i) q^{70} +(1.91027 + 1.38790i) q^{71} +(0.956080 + 0.694633i) q^{72} +(-1.02903 + 3.16703i) q^{73} +7.31486 q^{74} +(6.71081 + 0.648503i) q^{75} -8.65392 q^{76} +(-0.214612 + 0.660507i) q^{77} +(4.97854 + 3.61712i) q^{78} +(-4.18178 - 3.03824i) q^{79} +(-1.22570 - 1.87020i) q^{80} +(3.28304 - 2.38527i) q^{81} +1.86692 q^{82} +(9.97971 - 7.25068i) q^{83} +(0.347249 + 1.06872i) q^{84} +(7.63145 - 9.50525i) q^{85} +(-0.506408 + 1.55856i) q^{86} +(-1.36239 - 4.19302i) q^{87} +(0.257524 + 0.792578i) q^{88} +(-2.16491 + 6.66290i) q^{89} +(2.54961 - 0.694633i) q^{90} +(-1.17527 - 3.61712i) q^{91} +(-2.85599 + 2.07500i) q^{92} -8.09363 q^{93} +(0.674207 - 0.489840i) q^{94} +(-12.1147 + 15.0893i) q^{95} +(1.09089 + 0.792578i) q^{96} +(-8.97214 - 6.51864i) q^{97} +(-1.94851 + 5.99689i) q^{98} -0.984855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + q^{11} + 2 q^{12} - 13 q^{13} - q^{14} - 10 q^{15} - 2 q^{16} - 11 q^{17} + 14 q^{18} + 20 q^{19} + 5 q^{20} - 19 q^{21} + q^{22} - 3 q^{23} + 2 q^{24} + 30 q^{25} + 22 q^{26} + 15 q^{27} - q^{28} - 15 q^{29} - 10 q^{30} - 9 q^{31} + 8 q^{32} + 19 q^{33} - q^{34} - 15 q^{35} - q^{36} - 6 q^{37} - 15 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} - 19 q^{42} + 12 q^{43} + q^{44} + 15 q^{45} + 7 q^{46} - q^{47} + 2 q^{48} - 4 q^{49} - 5 q^{50} + 26 q^{51} - 13 q^{52} + 7 q^{53} - 25 q^{54} - 25 q^{55} - q^{56} - 15 q^{58} + 10 q^{59} - 10 q^{60} + 6 q^{61} + 21 q^{62} - 8 q^{63} - 2 q^{64} - 10 q^{65} - 26 q^{66} - 11 q^{67} + 24 q^{68} + 43 q^{69} + 25 q^{70} - 9 q^{71} - 6 q^{72} - 8 q^{73} + 24 q^{74} + 30 q^{75} - 10 q^{76} + 33 q^{77} + 23 q^{78} - 10 q^{79} - 17 q^{81} + 26 q^{82} + 27 q^{83} + 26 q^{84} + 5 q^{85} - 23 q^{86} + q^{88} - 15 q^{89} + 20 q^{90} + q^{91} + 7 q^{92} - 46 q^{93} - q^{94} - 30 q^{95} - 3 q^{96} - 36 q^{97} - 19 q^{98} - 42 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 - 2 * q^8 - q^9 + q^11 + 2 * q^12 - 13 * q^13 - q^14 - 10 * q^15 - 2 * q^16 - 11 * q^17 + 14 * q^18 + 20 * q^19 + 5 * q^20 - 19 * q^21 + q^22 - 3 * q^23 + 2 * q^24 + 30 * q^25 + 22 * q^26 + 15 * q^27 - q^28 - 15 * q^29 - 10 * q^30 - 9 * q^31 + 8 * q^32 + 19 * q^33 - q^34 - 15 * q^35 - q^36 - 6 * q^37 - 15 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 - 19 * q^42 + 12 * q^43 + q^44 + 15 * q^45 + 7 * q^46 - q^47 + 2 * q^48 - 4 * q^49 - 5 * q^50 + 26 * q^51 - 13 * q^52 + 7 * q^53 - 25 * q^54 - 25 * q^55 - q^56 - 15 * q^58 + 10 * q^59 - 10 * q^60 + 6 * q^61 + 21 * q^62 - 8 * q^63 - 2 * q^64 - 10 * q^65 - 26 * q^66 - 11 * q^67 + 24 * q^68 + 43 * q^69 + 25 * q^70 - 9 * q^71 - 6 * q^72 - 8 * q^73 + 24 * q^74 + 30 * q^75 - 10 * q^76 + 33 * q^77 + 23 * q^78 - 10 * q^79 - 17 * q^81 + 26 * q^82 + 27 * q^83 + 26 * q^84 + 5 * q^85 - 23 * q^86 + q^88 - 15 * q^89 + 20 * q^90 + q^91 + 7 * q^92 - 46 * q^93 - q^94 - 30 * q^95 - 3 * q^96 - 36 * q^97 - 19 * q^98 - 42 * q^99

Introduction

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